I might be interested in a cat sitting exchange actually.
We have a 6 month old called Maude who gets terribly lonely when left by herself. We try to make sure that if one of us is out, the other one will be there to play with her, but sometimes there is a bit of a gap....
We've live off Tower Bridge Road and we have used Susan Pugh's dog/cat sitting service (Paws'n'Claws") several times and been very happy with her. I think she pretty much covers all of South London. Her phone number is 0208 692 6591.
She was recommened to us by the Andrew Kirby Veternarian's office on Grange Road ( www.andrewkirbyvet.co.uk), BTW.
We have also used and would recommend Su & Peter Pugh - they charge £10 per visit rather than per cat, which is worth considering if you have more than one, as I think some services charge per pet. (pawsnclaws at btinternet.com).
However, I think they do fairly quick visits so if you want someone to sit and talk to the moggie for half an hour they might not be you people.
Sarah - sounds like you're making a rod for your own back never leaving the kitten alone. You should slowly introduce her to longer peiods alone so that she doesn't wreck the place or fret if there are occasions when she has to be alone.
She is left every day from about 9am to 5.30pm- its in the evenings we try and make sure one of us is in. If she's been by herself all day she looks forward to us coming home and i think it's unfair for her then to be left till midnight or something!
When we do get in there is such a fuss of purring and happiness when we open the door!