We do have an independent organization known as the NICEIC (National Inspection Council for Electrical Installation Contracting).
They offer certification for electricians, and certainly if you wanted work in major commercial projects or something like that then the chances are that the employer would require NICEIC certification. But it's not a legal requirement in any way.
Have a look at their website:
www.niceic.org.uk They mention Jersey having tighter requirements now, although how effectively they would be enforced is another matter. (For those unfamiliar with the British Isles, let me point out the Island of Jersey is British territory, but is NOT part of the U.K. -- They have their own laws, their own government etc.)
There are also no legal requirements in the U.K. for builders, plumbers, or any number of other trades to have official qualifications. As David says, somebody could have a tough time defending himself under Trading Standards Laws if he claimed a qualification he doesn't have, but that's a different matter.
Anyone fitting gas lines and appliances does legally have to be CORGI registered now. (COnfederation of Registered Gas Installers)