It could have worked at any time that was able to produce bigger sheets of flat reflecting metal, or glasses with reflective metal coating. It's all about the heat flux: Incident power per surface area.
This was very relevant in firebombing, and nuclear bombing, so the military made some tests (Lawson, "Fire and the Atomic Bomb"):
55kW/m² will ignite fibreboard in 5 seconds
25kW/m² will ignite wood "after prolonged exposure"
The sun will easily provide 1kW/m², so ideally you would only need 25 pieces of 1.xm² mirrors (.x to account for the angle of incident sun to target vector and the non-perfect reflectivity, probably something like 1.5) and some time. The 1m² rays do not need to overlap completely, a smaller area where they all overlap would be enough. the suns beams are essentially parallel, so you will not have to account for natural beam divergence - big BUT coming up, though:
BUT: This also explains the neccessity of "flat" mirrors: The rougher or more bumpy they are, the less of the original ray will actually strike the target - you will need to have as flat a mirror as possible - glass cast on liquid lead or tin will be very flat indeed, but i don't know if that method is applicable in pre-industrial times.
A pre-industrial method might involve small pieces of metal made extremely flat, that are affixed onto a shield and individually positioned by an artisan (occlude all others, have the shield in a fixed position and then, at noon, glue the piece in place and light up a specific target a bowshot away while the glue settles. Repeat for all little pieces, then you have a shield thats very accurate. now repeat for 50 other shields - typical pre-industrial drudgery by specialists. If the shield-fixator was cleverly built, the reflecting angle of the shield (i mean the angle between the affixed points and the virtual surface of the mirror) would be known, and you could construct a mechanical device that angled all the shields for a specific sun inclination and target-vector (The neccessary individual angles are all a function of shield position (on device), sun position (relative to device) and target position (relative to device), and the mathematical function would be (easily?) modellable by levers). You could even have a (probably multi-person operated, because mechanical) joystick and target/sun sights (like on a sextant) to aim. Might be even better than having humans hold the shields individually.
If you are not into big mechanisms, consider this: have a target buoy bobbing around in the targeted area. Have a foundation for every mirror-shield, have an ironsight (= annulus near the eye, many beads strung into field of view) one person is at the sights. have a sun locator (a stick in the ground, with a design drawn around it so the shadow can be located) with person watching it. Now target the buoy by lighting it up with one shield at a specific sun location&target (=buoy) location. the shield-mover now can sketch the shield position for that sun location and target location. Next shield. Next. As the target bobs around in the harbor, and the sun walks over the sky, the shield-movers will sketch a lot of sun/target combinations. These will correlate, thus giving them the means to guess at configurations for un-trained sun/target combinations. On the day of battle, have the sun-guy and the target-guy call out their readings, everyone else just moves their shields to the pre-determined positions.If we determine a "bowshot" distance (as per olden sources) to be 200m, 1 degree of error will displace your ray by about 2 metres. With 1m-diameter rays we should stay below 0.5m error, so 0.25 degrees would be the maximal acceptable error. Is that achievable? For a circle 2m in diameter, 1° of circumference is about 2cm, so 0.5cm error for the tip of a stick attached to the shields. achievable, i'd say.
A pre-industrial source for ultra-flat surfaces might be crystals, but i doubt you'd get enough crystal-faces for the area needed. But even the ancient Egyptians had hand mirrors, and those definitely need to be flat, so i guess they had some experts that could make them that way. If you know of a method to get any hard substance really flat, you can always cover that in gold leaf (very ancient material too) and polish it, so pouring ceramics or something might work also, you'd just need one super-flat mould.