The British Empire was vast and I can't come up with a definite answer for all the areas that were colonized by them but in my country "Egypt", they didn't do that. They however facilitated the work of western missionaries but it didn't achieve much with the Muslim locals and probably contributed to the outrage of Coptic clergy as these missionaries were snatching people from their congregation. Other than that, the British didn't really care about religion and their social order was constructed on race/class first basis and anything else second while for the Ottomans it was all about religion first and anything else second.