I would like to tour the UK and Ireland next year. I plan to visit for about 3 or 4 months. I would like to travel as cheaply as posible and was hoping I could buy a vehicle upon arrival, keep it for 3 months, then sell it before I return to th US. I would be traveling alone and I was hopeing I could sleep in the vehicle at least part of the time. Does anyone see any unforseen problems with this scenario? I would like the smallest and most inexpensive to operate vehicle posible that had a flat area 6 feet long that I could sleep in. Any suggestions?
Marshall

I believe in order to purchase a car in the UK you may need to have a permanent address there, otherwise where would the DVLA send the logbook (ownership papers) to? Check out the DVLA website, Short Description of URL Content Also, you need to ensure that you can use your foreign license to obtain suitable auto insurance (you can't tax a car on UK roads without insurance, and if you drive on a car that has no tax you will be picked up and the car possibly confiscated, ie destroyed). If you have considered all those options then go ahead, try out www.autotrader.co.uk, but if you haven't considered the above mentioned options, it sounds like you need to think the situation through more thoroughly. Sorry to rain on your parade ...
I forgot to mention - nobody will stop you from sleeping in your car, but it would be awfully cold and somewhat uncomfortable ...

I'm not sure actually that 'no-one will stop you from sleeping in your car'. If you're in the middle of nowhere, fine, but if not I can see you getting told to move on by the coppers. You'd have to choose your sleeping places carefully.

And if you do sleep in your car don't do it whilst drunk with the keys in your habd/the ignitition. English law can class this as being in charge of a vehicle whilst over the limit. Rare but not unheard of.
- A decent, reliable car/van will set you back £1000 - £1500
- like this one
2. Insurance for 3 months will be very difficult (but not impossible to get), premiums will be very high especially seeing you're foreign, you have no driving history in the UK, you have zero no-claim bonus, you're insuring for a very short period of time and you do not have proof of residency - this is key to getting insurance in the UK, actually it's key to doing anything that involves the law in the UK.
3. Petrol is expensive, average 95p (USD$1.92) per LITRE (not per gallon)
Suggestions:
If you must drive, would be cheaper to hire a camper van like wicked campers. For 3 months with wicked campers (not inc. insurance waiver, assuming there is one) you can get a 2 berth van for £900.
You can still travel by road in the UK very cheaply and quickly without driving yourself. You can use coach services like National Express and Mega Bus. Train travel can also be a cost effective way to see the UK without flying (if bought wisely ie in advance, non-flexible tickets, etc). As for accommodation using these alternate travel methods, B&B (Bed and Breakfast) average around £25-30 per person per night and sometimes less for single occupancy. There are also plenty of hostels about of course which are probably (on average) cheaper than your B&B style accommodation. Of course that will all probably work out more expensive than having your own, portable accommodation.

#4...and they take that very seriously. The only way around that is to unlock the car and go hise the keys somewhere nearby. If the police then check you, in theory, you are unable to operate the car...however I would not like to try it!

Last we tried (5 years ago) we were unable to get insurance for less than a year - the good old temporary month by month insurance days are long gone. If you had to insure the vehicle for a whole year it would make it even more expensive!
I dont imagine that it would be high on your priority list, but you are not allowed to sleep in your car overnight in most motorway service stations (petrol stations).
Most of them have notices in the car parks to say "no overnight parking", and they hire security guards to patrol the parking areas.
I have a friend who was driving the length of the country overnight and got too tired to go on driving. She pulled in to a service station for an hour long sleep in the drivers seat, and woke up to find a parking fine on the windscreen. She was mighty cross about it too.