I have a 1997 P38 Range Rover 4.6 (in low key AA yellow) which I bought new when we lived in the US and brought to the UK when we returned in '02.First, shipping is pretty cheap on a ro-ro from a majo port like Newark (shipped my new 2008 Range Rover G4 there and back from Southampton for 3 months this summer, about £1,000 there and $1,000 back). There are a lot of forms to fill and use of an agent is money well spent.
I am usure bout the tax implications for foreigner bringing in a presonal import (I was able bring in my car tax free as I had owned it overseas for over a year and was returning to UK tax residency). On this basis you too could probably import tax free.
If you choose not to bring in the car as a permanent import but instead just come in as a visitor (i.e. keep it on US plates), you can do this for a year before you have to decide whether to register it in the UK or remove it from the country. Frankly, I'd be surprised if anyone was counting the days and if you do decide to take the car back to the US after a couple of years the're not likely to stop you from exporting it... Be aware though that Her Majesty's Customs have much more Draconian powers than the police, so if they were to pick up on a vehicle that had overstayed its welcome they can immediately impound it. That said, they are generally focussed on a much more important day job in countering drug runners and terrorists.
Getting a car registered is a bit of a pain. You have to go to an inspection centre (of which there are few, dotted around the country) and get a single vehicle type approval certificate because although your car was made in the UK it will have no EU type approval and most critical components - windscreen, seatbelts - have only US DOT rather than EU approval marks. The testers at the centre I went to were very friendly but were flummoxed to see an essentially British car before them - all the other vehicles awaiting their attention were grey market Mitsubishi Evos and assorted Chevy Corvettes and Hummers. I had changed the headlight units to RHD ones and had the front indicators rewired so they are not permanantly on at night. The latter was essential, the former optional (stick-on beam deflectors ar apparently permitted). There was a bit of bickering over the DOT marks - at one stage some clown told me I'd have to replace the windscreen, seatbelts and airbags with EU marked ones - but he was overruled by his suprvisor and I drove off an hour later with type approval certificate.
Parking in London is a pain and, as pointed out, can be expensive. There is also a £8 a day congestion carge if you drive on weekdays in central London (not due if the car does not move!). Petrol prices will astonish you. The good new is that British insurance companies are unfazed by foreign registerd LHD cars, so you can get a competitive deal. I had a huge issue getting a foreign registered RHD (and non-EPA approved diesel!) car insured in teh US - good job I still have a US license). Oh yes- you'll need to pass a driving test within a year too.
A subsidiary benefit I found was that while the car was still on US plates I was pulled over a couple of times for modest speeding... and was let go each time after a suitable display of contrition with a warning (rather than fine and points, which I would definitely have got no doubt with a UK car with less paperwork involved).
When I was at the LSE myself many years ago I struggled to run my MG and ened up downgrading to a Citroen Mehari, but I'm sure an economist can calculate the costs involved.
If you want to sell the car here, I think you'd struggle to get anyting much for it unles you'd registered it. I estimate the value of my immaculately maintained, LHD, 150k mile yellow monster to be close to zero unless I were to luck out ad find someone who really wanted it. But that's what orums like this are for, I guess.
Let me know if you want shipper and agent suggestions.