Addison Lee used to, but have stopped. However, some of their older vehicles might have one, worth asking.
There was a thread about this recently.
http://www.nappyvalleynet.com/post19463.html#p19463
I recommend a chap called Hanif. He's local and definitely has an infant seat. I originally booked him through a cab company (can't remember which one) for a friend of mine and her 1yr old. She told me afterwards how impressed she was with him, and he gave her his mobile number for future bookings. I put his number on the other thread.