The British are always talking about multi-region mods in their magazines. It seems that the British do not think that buying a single region DVD player is a good idea. Some players have chips that are replaceable, others have sets of switches or leads that can be cut. You need someone who knows how to modify your specific DVD player.
Since modifying DVD players is so popular in the U.K., there may be some resources on the internet that tell you how to do it for your player. Try this search:
Go to google.com and click on the advanced search
Restrict the domain to co.uk
Search for DVD hacks
It would probably be easier to buy a multi-region or U.K. region DVD player from a U.K. source than to modify your existing player. Amazon.co.uk sells multi-region players but they are restricted to shipping them the U.K. or Ireland. They may sell and ship a U.K. region player to you though. You may want to pick up a magazine like What Hi-Fi and call some of the big electronics mail order advertisers. I don't think you'll find it too difficult to find one who will ship you a multi-region player, or maybe a U.K. player that is easy to modify. If the only foreign DVD's you want to play are from the U.K., then I think a U.K. region player would be the cheapest and easiest route.