Many of the combination washer/dryers are the condensing type too. Cold water is run through a finned element over which the hot air from the dryer exhausts. The water vapor condensed on the element is then pumped out along with the cooling water via the normal washer drain hose. The arrangement works, but of course the dryer uses huge amounts of water in the process. If you're on a metered supply, that could become significant.
Some separate dryers are intended to just vent into room in which they're located, but these can result in a big vapor/condensation problem in the room.
The typical U.S. dryer runs on a 240V 30A hookup, which allows high-power heating elements -- up to 7kW -- to be used. The majority of British dryers are designed to run on a normal 13A plug, limiting the elements to about 3kW maximum. Larger versions are available, but will need to be wired on a dedicated circuit which is not provided in most homes, so you'll need to allow extra for its installation.