I've tried googling (and direct access to all of the usual places to look for hacks) and I think that you might be out of luck.
The manufacturers of DVD players are bound by licensing restrictions to ensure that they'll only work in a single region. At one time they used to make every player 'multi-region' and then tweak it at the final stage so that it only worked in just one part of the world. That final tweak could be undone if you knew the relevant hack. However the holders of the licensing rights (which basically means the big film distribution companies) now insist that manufacturers make players which, from the very start, can only be used in a single region. So there are no hacks possible for recently produced DVD players.
However eBay still has plenty of offerings which can solve your problem fairly cheaply. e.g. (if you don't mind a few scratches on a 'Grade B' product) you can buy one of these for £15.95 (with free postage):
http://www.ebay.co.uk/itm/Grade-B-Polaroid-Compact-Multi-Region-DVD-Player-SCART-Region-Free-0-1-2-3-4-5-/282023279835?hash=item41a9e5bcdb:g:NYQAAOSwA3dYe4kc
(There's a 12-month warranty and the seller has excellent feedback. If my own region-free player packed up that's what I'd go for)