Think you are a little bit confused... the EIC (electrical Installation Certificate) *is* your certificate, if the work didn't involve any new circuits a NWC (minor works certificate) could have been issued
An electrician is registered to self certify electrical work as required by the recent 'Part P' of the building regulations, but when they do so, they are also certifying that the work complies with *all* building regulations (parts B and L among others are relevant here)
The following bodies run 'full scope' schemes for the above: Niceic, Napit, Elecsa, BSI and ECA (BRE), the rules of these schemes require compliance with BS7671, which requires certificates as in the first paragraph to be issued (of course it would be pretty daft to go against BS7671 on the whole anyway!), the contracter than can tell their scheme about the work, and they will tell the local authority that they don't need to worry about it