Sandra ia correct. It's not illegal to own and use a multi-region DVD player in the UK. It's also not illegal to import DVDs into the UK from other countries, but it is illegal to sell them, which is why any UK retailers selling Region 1 (US) DVDs in this country, either ship from abroad, or claim to be merely an agent importing the goods for you.
Region 1 - The U.S., U.S. territories and Canada
Region 2 - Europe, Japan, the Middle East, Egypt, South Africa, Greenland
Region 3 - Taiwan, Korea, the Philippines, Indonesia, Hong Kong
Region 4 - Mexico, South America, Central America, Australia, New Zealand, Pacific Islands, Caribbean
Region 5 - Russia (okay, former Russia), Eastern Europe, India, most of Africa, North Korea, Mongolia
Region 6 - China
Regions 7 & 8 are reserved for other purposes.
Be aware that if you import goods exceeding the value of £18 (including / excluding shipping costs is a bit of a grey area), you are likely to incur UK customs charges and VAT, so keep your orders down to one DVD per order, unless you can get exceptionally cheap ones.