Here's what I would do. Please apply liberal amount of Google prior to consumption.
1) Buy a Zagat guide and go spend a lot of money on food - London now has some fabulous restaurants, and since you will be on expenses (?) get out there and enjoy it.
2) Museums! There are a great deal of museums in london which cater to all sorts of different tastes - The science museum, Victoria and Albert, National Gallery etc etc. There are also some boutiquey modern art museums like the Saatchi gallery which has oddball modern stuff. The Tate, Tate Modern and the British museum may also be interesting.
3) Tourist crap! Go see the Tower of london, Buckingham palace, Picadilly Circus, Trafalgar Square, Hyde Park Corner/Marble Arch, and probably a bunch of other things I forgot.
4) Rent a car. It is possible to rent an elise in the UK - and if you are a major psycho you might be able to rent a radical. If you are a little tighter on the budget, Budget (I think) has the Ford Mondeo ST200 - which is a 200HP car one class up from a focus. They go like stink and are fun to drive. There are racetracks.... Brands Hatch, Silverstone, Castle Coombe - find out whats on when you are there and head out if theres something interesting. You might want to drive to Beaulieu Motor Museum (
http://www.beaulieu.co.uk/ ), or you could try and get on a Lotus Factory tour in Hethel, Norfolk. You could go see Stone Henge, or the underappreciated Avebury stone circles and other random crap during your trip. You could event go see Andy in Bristol! The South West, (Devon and Cornwall) although tourist traps, are very pretty and get the best weather in the country (generally - YMMV).
It's also quite viable to travel by train if you wish.
If you want mondo points with the wife - buy her a ticket to Paris and take the chunnel down to meet her.
Bars generally shut at 11:00 - but there's plenty of nightlife to be had.
CARSPOTTING - Be on the lookout for Lotuses, Aston Martins, Bentleys, Radicals, etc etc.... there are lots of makes and models you won't have seen before, and some of them are quite interesting. Car of the Day for today is the Citroen Xantia Activa - a midsized sedan that never experiences more than .5 degrees of body roll thanks to active suspension. 30% extra traction out of whatever tires you put on it.
I'll let you know if I think of anything else.