The centaurs would have the same technology as the British, more or less. Would they simply find squares unbeatable, unless they can bring up artillery to shoot them?
I wouldn't say unbeatable, but... being a horse with hands just isn't that big of an advantage.
- Centaurs are big targets. They can be seen from further away, and are easier to hit from further away.
- Centaurs are vulnerable targets in a way that human cavalry like curassiers and dragoons are not, because those two kinds of soldier can keep on fighting when their horse gets shot out from underneath them.
- Centaurs are too big and unwieldy to make as good a use of cover as humans, making them potentially more vulnerable to skirmishers and ambush.
- Centaurs are a logistical nightmare... they're big, and that makes then hard to transport and expensive to feed. They'll often be outnumbered by humans as a result (and indeed, the use of infantry squares against them kinda underlines this).
- Centaurs may be more readily equipped to bring light artillery to bear than mere humans, but they're also more vulnerable to artillery fire than regular infantry (on account of being big).
In cases where centaurs find enemy infantry in square, and don't have artillery they can bring up, what could they do to fight a British infantry square?
The same thing their cavalry equivalents such as curassiers. They won't outnumber the infantry and they can't charge in to a square ready to receive them; to try and fight in those circumstances would be extremely foolhardy.
Infantry squares are a bit slow and unwieldy and being bogged down they may have been prevented from achieving some other strategic goal, or are now at risk from other incoming forces friendly to the centaurs. If the infantry break up their formation to move more quickly or to bring more guns to bear on other forces, cavalry are well placed to deal a killing blow.
In the absense of support or opportunities to force the square to break formation, the centaurs can simply fall back and live to fight another day.
To respond to a separate comment above,
This also suggests they simply cannot attack squares to the extent where they should not fight in field battles
Cavalry were used, often effectively, against armies that included gun-wielding infantry right up to the first world war.
They were a valuable and useful part of the armies of the time, but they were only a part and needed support of infantry and artillery. Unless your centaurs somehow have the advantage of numbers (which would be surprising; they'd need a fearsome agricultural economy behind them to feed all that horsemeat, and such a thing would be vulnerable...) then they'll need to be part of a combined-arms force, just like their opponents.