I suspect that some of the responses above may be a bit confusing for the OP (and Greenie9657).
As has been said, anyone can undertake notifiable work, with or without any qualifications. However, unless the person concerned is a member of a self-certification scheme (which does require them to have qualifications), such as NICEIC etc., they can only do it (legally) by notifying the LABC, paying the LABC fees and the work being subject to 'inspection' by the LABC.
If an LABC is satisfied about the competence of a person (a judgemnet likely to be made on the basis of qualifications) they may accept certificates (and test results etc.) provided by that person, and there then may be a reduction in the fees charged (and 'inspection'undertaken). However, if the person is not a member of a self-certification scheme, there is no way of avoiding notification, and at least some LABC fees, for notifiable work.
To comply with the law, all electrical work, whether notifiable or not, has to be undertaken in compliance with Part P of the Building Regs - which essentially means that it has to be done 'safely and competently'. In theory, LABC can take action in relation to non-notifiable work which is not compliant with Part P (i.e.'unsafe') but, in practice, they will virtually never become aware of such non-compliances.
Kind Regards, John