The most common place by far is Switzerland. France, Isle of Man etc allow the ownership of handguns, but only by residents. Switzerland allows non-residents to buy and own guns (and handguns), so Britons can live and work in the UK and travel to Switzerland to practice.
For London 2012, special permission will be given to competitors to allow them to being handguns into the country.
Trap, skeet and rifle competitions are no problem as shotguns and rifles are legal (heavily restricted, but you can get them if you really want to).