Yes, they were. The 1907 Manual of Military Law does allow British men of non-European ancestry to enter the British Army, but what's even more impressive is that there were a considerable amount of black British officers as well, something that was outlawed according to the King's Regulation. I've spoken a bit more in-depth about this in this post about black British officers who served during the Great War which also speaks about some of the issues of source material in this context. I would be more than happy to answer any follow up questions.

I've been looking for pictures of black and white British soldiers together in trenches in WW1 and I couldn't find any. Does anybody know where I can find any photographic evidence of this occurring?

Anyway, regarding the Sikh Sepoys, wouldn't they be serving with their own units?