Who should connect the electrical wiring on a new boiler, gas engineer or electricain

depends if the socket or fused connection unit for the boiler was already there or a new installation. If already there, gas engineer can do it, if its a new circuit, electrician should do it, and issue a minor works certificate.

electrician if you want a certificate

Either provided that they are registered under part P of the building regulations and can issue a self certification test certificate for the work they have carried out.