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Background:

In an alternate history of the island that became modern Britain, prehistoric humans entered the Bronze Age but then (for various religious reasons - the full details of which are probably not pertinent to the question) decided it would be abhorrent to start dabbling with any other metals. Essentially, copper was deemed sacred while all other metals were considered profane and were banned (including in trade with mainland Europe). It is deemed acceptable to use a little tin to make bronze, but only where copper alone would be insufficient for a given purpose. Tribal leaders, nomads and even solitary hermits up and down the island share in these beliefs and enforce them as best they can. Even pure tin products themselves are prohibited; tin is only allowed to be used in the manufacture of bronze, making up no more than ~20% of the final alloy.

The ban is successfully upheld for thousands of years (aside from, one would assume, the odd smuggler dealing in small pieces of iron and steel contraband every so often) until the Roman occupation of Britain. At this point, groups of these bronze-loving people retreat into magically isolated parts of the country (in groups by the dozens or hundreds) to continue life without iron and other metals. The secret communities are able to easily trade and communicate with each other but remain undisturbed by the Romans and subsequent invaders. Put simply, they live and work in areas of Britain that are undiscoverable (not unlike a Harry Potter Fidelius charm or a Doctor Who perception filter), and they can source their copper, tin and other materials from these places in the same way as they normally would.

Question:

Presumably these constraints result in a ceiling effect as far as technological advancement is concerned, but how well could a bronze-based society actually develop before hitting their limits, if we allow them to freely use substitutes (copper, bronze containing only tin, or non-metals) where we would ordinarily use iron, steel, lead, brass, and any other metal or alloy? Specifically, could they make it as far as The Georgian/Victorian period? I should say, I don't need them to be able to harness electricity; they abhor that just as much as iron and steel

One thing to note: I'm happy to take a bit of creative license with geology here and state that availability is not a limiting factor. This is an Earth where copper and tin are as abundant as we need them to be to facilitate technological advancement. I'm more concerned with whether bronze's physical properties are actually fit for purpose. From what I've read, the reason prehistoric man graduated from bronze to iron was mostly down to the ease of sourcing and processing the latter, rather than the discovery of any superior physical properties (at the time, anyway). That answers my question for the first few hundred years of slow technological growth, but I'm wondering if a bronze-only society begins to fall down by the time we hit the middle ages or industrial revolution, where technology gets arguably more dependent on various alloys and their respective properties.

There are a few specific technologies I'm particularly unsure about, though I'm a new face here and perhaps it would be considered too broad to post a list of them. Perhaps not. I'll leave it here for the time being but happy to edit it out if it's not appropriate:

  • Gaslamps (and, by extension, gas manufacture or natural gas extraction)
  • Indoor plumbing
  • Steam locomotives
  • Early firearms
  • A sewage system
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  • $\begingroup$ Very difficult to build firearms and steam engines out of copper. They use steel for good reason. $\endgroup$ – user535733 Oct 29 '17 at 18:46
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    $\begingroup$ If copper and, much more importantly, tin were abundant on Earth the normal civilization would have used bronze in preference to iron up to the discovery of industrial processes to make steel in the 19th century. So yes, obviously, they could reach 18th or early 19th century technology. Unfortunately on this Earth tin is rare... For example, firearms were made of bronze up to the 19th century; copper indoor plumbing is still in widespread use; gaslamps were most usually made of glass or bronze; and sewerage systems were normally made of brick until the advent of reinforced concrete. $\endgroup$ – AlexP Oct 29 '17 at 20:35
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    $\begingroup$ I suggest that it might be easier to engineer your world with the abundances of materials that you want rather than try to magic away the problems caused by iron in our world. Perhaps iron is present at low levels but without any ore deposits. $\endgroup$ – Slarty Oct 29 '17 at 21:02
  • $\begingroup$ Your biggest issue is industrial machinery, copper (and "pure" bronze) has crap wear resistance, meaning things like mills or or bearings made of copper wear out incredibly fast. Once you you start getting large powerful machines or small intricate ones copper use not going to work. You really need tri-metal bronze and brass to make these kinds of machines. $\endgroup$ – John Oct 30 '17 at 1:45
  • $\begingroup$ @AlexP Even steel is not necessarily superior to bronze. It's only the cheap availability that makes it more widely used. $\endgroup$ – Ash Oct 30 '17 at 10:41
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Oddly enough for all things on your "unsure about" list copper alloys would be quite acceptable. In some cases better than iron based alternatives. Most of these are things where iron is used because it is much cheaper than copper.

The big problem is IMHO tools. Since copper is softer, copper-based tools will deform and wear down much faster. This would go double for any kind of powered machinery. And it will become an issue surprisingly early. Iron axes or ploughs are better than their bronze counterparts. Although historically being cheap enough to be available to normal people was probably the biggest advantage.

It is difficult to predict the effect of affordable copper and bronze, especially since technological advancement is largely driven by economics. Much would depend on what makes copper affordable to them.

And that is not the only unknown variable either. How large is their population? What is their transport system like? How much food can they produce? What is their surface area? You need certain "mass" and density of people to develop and sustain industrialization.

Also the "undiscoverable Britain" pretty much requires magic. This would probably make a huge difference.

And, obviously, it is very important to consider how connected they are to the outside world. Any amount of trade, no matter how discreet and well controlled, will give the people access to benefits of the outside technological progress and economic growth. If you know that somebody outside built a steam engine, duplicating it using approved materials requires much lower technological and economic base than the first invention. If you can buy food from outside, not having proper ploughs is not that much of on issue. You can even import your bronze tools or copper pipes mass produced from outside factory. (Probably a good idea, it should keep all that infernal pollution out.) You can even produce and sell your own products on external markets and avoid the problem with your own economy being too small to support industrial economy.

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If you can just make bronze with varying amounts of copper and tin you have alloys with a vast spectrum of mechanical and physical properties, some of which may favorably compare to even steel. In fact, bronze-llurgy :) is all you need.

One of the historical reasons of the switching from bronze to steel in Europe has been geology. Major tin suppliers were not typically located within the continent. On the other hand, iron and coal are rather abundant. If you remove this constraint, steel may become unnecessary until the very late XIX century, when the high-temperature furnace technology led the way for handling other types of materials.

Relative to your list:

  • Gaslamps (and, by extension, gas manufacture or natural gas extraction): while the melting point is not as high as carbon steel, bronze will not melt easily when used as caging for a gaslamp. I am not familiar with the mechanical properties required in gas extraction, but as long as it is about making pipes and pressurized containers, there should be no issue in replacing steel with bronze. Recall that the latter was used for cannons, and it is thus capable of withstanding fairly high pressure and high temperatures. Also, given that bronze makes strong blades, I would not be surprised if it could be used for drill-bits.

  • Steam locomotives and Early firearms: early firearms were indeed made of bronze, cannons in particular. This suggests that the material could also be suitable for holding together a steam engine. Note that today we use bronze for hard-wearing bearings.

  • Indoor plumbing and a sewage system: relative to steel and iron, bronze is less easily corroded and should last longer when used for plumbing. Today still, certain pipes for heating buildings are made of copper alloys.

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Gas lamps
I don’t see any problem with building a copper gas lamp. The apparatus for processing the gas might be a little bit more problematic and the shape and size of equipment might be different but it should still be doable.

Indoor plumbing
Could be achieved but would be difficult unless a little tin solder was allowed. If no tin is allowed for this purpose then a copper compression fitting of some sort should be possible, but might take longer to develop. In the early stages piping might be limited to what could be installed in one piece. Another option would be to heat a copper sleeve around a joint and then crimp it slightly.

Steam engines
I would have thought steam engines could be made out of copper http://www.alspcs.com/Copper.html There is a steel rod in this one and some brass fittings but I imagine these could be reengineered in copper or bronze and made over size if necessary. For instance the diameter of the piston rod could be the same width as the piston head. That said I imagine there would be more mechanical failures and a much lower pressure and efficiency.

Early firearms
Yes again. Bronze was used to make early firearms in our world.

Sewage system
Basic brick lined tunnels would work at the most basic level. It depends what you want. Pumps are possible, settlement tanks and air blowers should be possible.

Summary
All of the items you mention should be buildable. But they might be harder to install or develop out of synchronisation with our time line (indoor plumbing), work much less efficiently (steam engines and fire arms).

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I would suggest (in agreement with earlier posts) that all of the technologies you list are indeed possible with the given restrictions. I also think it is unlikely. If there is a set of religious ideas that constrain thought against certain metals then investigating the metallurgical ideas into making a pressure vessel (needed for steam engine) is likely to be either outside a typical researchers worldview at best, considered heresy at worst. This would mean that metallurgical advances wold be mostly by accident and take a lot longer.

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