I've just changed jobs so I'm contemplating selling mine (due to increased commuting miles)
It's a 2000 car, silver with black/cream leather which is very clean (the cream part of the steering wheel has suffered the usual fade that I've seen on all I looked at)
The car has just turned 98k miles and drives as it should. Doesn't lack any power and has averaged over the last 1000 miles 22.8mpg (did manage to get 31mpg on a recent run!)
The climate control doesn't work (I've never had a car with a/c so it doesn't bother me) but it's probably more than a re-gas though unfortunately as it shows zero pressure when using the climate system to diagnose.
4 matching Michelin tyres, with the correct speed rating etc with >4mm on
I have had the rear cats and resonator removed to unleash the v8 sound, but for normal cruising it's not much louder than standard.
The satnav and phone all work, although the tv no longer works since the digital switchover. The electric seats, heated elements and orthopeadic controls all work perfectly
The car does have a small rust bubble under the boot lock (as most do) however it hasn't changed at all in the time I've had the car.....and also a 'scuff' on the front bumper (drivers side corner) where a 'rock' was chucked up by a passing people carrier (scary moment when it was flying towards me, but it only resulted in a scuff)
Unfortunately for your requirements regarding London, I'm just outside of Glasgow (plenty of cheap flights though!) but I am towards the lower end of your budget. If I was to sell the car, I would let it go for £4,000 (if I decided to advertise it, I'd realistically be looking for £4,800 based on other cars for sale on the market
If you want any more info, give me a shout