As has been said it is possible to get a few multiregion BD players, (although be careful as some say in the small print that they are only multiregion for DVD not BD), for <£200 they still can be quite expensive. The Toshiba Alex mentions is a reasonable option although I do know some people who have been unhappy with it as a player (in general not due to the multiregion aspect).
Personally I have two Panasonic BD players which are multiregion chipped for DVD and BD but they both cost me more than the £200 amount when I purchased them. The place I got mine from does have the Panasonic BD75, chipped, for less than that amount though, and if it uses the same mod as my older models then it will still allow normal firmware updates. I can't say where from as they would be classed as a competitor.
A hardware mod for a normal player can add £80-150 to the price above an un-modded player.