Multi-region players are increasingly hard to come by. At one time all DVD players were manufactured as 'multi-region', with the region coding added being added at the end of the process. That meant that the encoding could easily be removed if you knew the hack to do it.
However film companies clearly weren't too happy about that, as it made it harder for them to sell their distributions rights separately in different areas of the world. So they've used legal pressures to insist that modern DVD players are manufactured in such a way that they can only work in one region, with no way of hacking them to multi-region capability.
However a few multi-region players are still available on both Amazon and eBay and there's no need to spend a great deal of money. For example, twenty quid (including postage) will get you one of these. (Both the product and the seller have excellent ratings):
http://www.ebay.co.uk/itm/Polaroid-Multi-Region-Free-Full-Width-DVD-Player-Remote-Regions-123450-SCART-/182423957539?epid=1279217490&hash=item2a7950b023:g:T-cAAOSwSlBYuVpd
(Note that it uses a Scart connection, rather than an HDMI one though).
An alternative, for about the same money (but still 'Scart only') is this:
http://www.ebay.co.uk/itm/Blaupunkt-DV2202-DVD-CD-Player-Multi-Region-Region-Free-0-DVD-/122487665431?epid=1585218474&hash=item1c84d57317:g:v9YAAOSw1WJZEkq6
(Again, good product & seller reviews)
If you really must have HDMI, this is what I'd go for:
Amazon.co.uk User Recommendation