I'm afraid my answer will be nothing more than anecdotal. My source is that I lived in London for a while. The bottom line is that no tip is required. However some people do tip, as it often happens in these cases, be it for habit, or because they feel they have to.
With minicabs (in London) I always agreed the fare in advance, and made sure the driver did not attempt to squeeze a few extra pounds from me by quoting him the price before paying. Anything as simple as "It's £15 right?" will do the trick. I usually never tipped, unless the driver provided an extra useful service, such as helping me with heavy luggage for example. This last consideration applies to minicabs outside of London too. I also tipped one particular driver, who picked me up so many times from Heathrow that I used to ask for him specifically when booking.
As far as I remember I never tipped a black cab. I certainly never tipped 10%. I always thought of the cost of the service being so high that no tip was needed. I never heard drivers complain about this. Maybe I was (am) just cheap. Or maybe it's just the way I am used. Moreover, now that card payments are widely used, I don't even know if there is an option to add tip before paying.