Hi there,
Welcome to the forum!
I suggest you nip into WhSmith and pickup a copy of 'WhatCar' magazine. All the various options that are available to you will be listed here. Cash, bank loans, various Leasing options etc are all covered.
I'm presuming you are American and newly arrived in the UK, so some of the options may not be available to you. Only you can see your financial position to see what you do indeed qualify for.
You can then look into buying privately, from a independant car dealer, a main authorised dealer, buying from an auction.
You'll also need to take into consideration what kind of car you want, Diesel, Petrol, small city runabout, mid size car, hatchback, executive saloon etc etc, potential insurance costs, then the usual costs for the annual MOT check (£30-50) and which Road Fund License band the cars you are considering fall into (from zero to around £450/year)
Cheers, DtM! West London & Slough UK!