As for getting shoes soled, I think there's a place on Tower Bridge Road up by Manze's pie and mash shop, but could be mistaken. If I am, then I think nearest place would be Elephant & Castle shopping centre.
Someone else might know a cobbler (is that the correct phrase?) closer though.
There is another car wash, "hand car wash"-esque rather than machines, as much as any are these days, on Southwark Bridge Road opposite the Island Cafe. Its mainly used by taxis and chauffer cars which I normally think is a good sign.
I think its either £5 or £10 for the outside, cant remember which.