When I had my own black cab I'd use the one in Southwark Park Road by John Bull arch, opposite the garage at the junction of Drummond Road.
They always did a good job, £7.00 inside and out then, don't know how much now.
The bonus for me was that they'd charge me black cab rates for my wife's people carrier, or she'd get charged black cab rate if she went in on her own, but wore my green badge around her neck.
I just wanted to reiterate how good the hand car wash on Grange Rd is. I took a car covered in green mould there (it belonged to my dad who died earlier this year and had been standing in his drive unused for six months). They only wanted to charge £10 for cleaning it inside and out but I gave them an extra fiver as they did such a great job. Came up looking like new. The guys there are really hardworking and polite and the manager always has a smile on his face whatever time of the day or evening you roll up.