Hi Dar!
Nip into WHSmith's and pickup a copy of What Car?! magazine - in there you'll find allsorts of reviews and more importantly, overviews of all the different ways to buy a car in the UK. I have a feeling most of those ways won't actually suit you - but at least you'll know a little more and might be able to wangle finaances in order to meet criteria.
Of course, the usual 'if you've got the money you can buy' adage rings true. You could of course, do a little research, find yourself a 'cheapy' car say for around £500-1000 and tax, insure and MOT it, for comparitively little outlay - this will give you the advantage of building up your own no claims bonus too.
Cars nowadays are 'proportionally' cheap in terms of buying - get a 3-4 year old Fiesta or Corsa for little money and chances are if it was some woman's shopping & kids trolley it'll have low miles as well - low miles isn't a guarantee it'll be a 'good' car - but it helps.
Buying the car like that means you may not have to jump through hoops as a new arrival into the UK.
If yer better half buys, that'll be a route to take, remember to get an appropriate insurance quote to cover you.
whilst you look at cars, even though it'll be on the expensive side - you 'could' hire cars out on your USA license for longer periods of time to at least help you be mobile and possibly go look at cars that come up that are some distance away (that always happens!)
What kind of car do you have in mind?!
Hope this helps - Cheers, DtM! West London & Slough UK!