I've been a few times with work, three / four times a year in a normal year.
Never stayed anywhere other than top notch hotels so can't comment on apartments etc. Although I do have a guy that works for me who is now based out there three months at a time. He seems to love it although it took a bit of time to get him settled into a decent apartment.
As a city it's like all other big cities, it has good bits and bad bits. I'd suggest not being there during the monsoon season if you can avoid it. Every time I've had a stomach problem has been during monsoon season visits.
Culturally India is an incredible country (some decent riding to be had too), there's something of everything. The people are very welcoming and friendly, more restrained and stand offish in the north but more chilled in the south.
Mumbai's very multicultural now, partially due to the presence of Bollywood and that means you'll not struggle to find other UK people to build a network of friends. You can get UK beer if you want it, I've heard a rumour of an Irish bar but have never managed to find it.
If I had the chance of an extended trip, and didn't have a wife and kid on the way I'd jump at it.
Great experience and a great country, go for it!
Drop me a line if you want to know more or specifics