There are many varied routes to becoming an 'electrician' as its not a restricted trade such as a solicitor or dentist.
A time served electrician is somebody who carried out an apprenticeship, followed by a technical assessment known as the AM2 as part of a level 3 NVQ.
Other people may have other experience, such as a military technical background or other closely associated trades and registered with a competent persons scheme who assess them on an annual basis. These schemes are known as competent persons schemes.
The skills to join one of these is not that great.
Ultimately, any electrician should have sufficient skills and experience, I cant emphasise the experience part enough. Ask them for copies of the insurance policies, examples of recent work/references. Ask if they are part of a scheme such as NICEIC, Napit, stroma etc.
Some work is notifiable to building control under Part P of the Building Regulations, failure to use a suitably registered electrician can lead to a £5000 fine to the homeowner! This only applies to things like rewires, new circuits or work in locations such as a bathroom
Any reputable electrician will not mind being asked for this information.