the new incoming electricity supply cable was installed by the electricity company, or the National Grid contractor?
Whenever a new main and meter are installed the electricity supplier needs to be satisfied that the house installation is safe, and that includes an earthing test - they won't connect a supply until/unless this has been done.
Your son and his wife would have needed building regulations approval (and planning consent) for the conversion, and the local authority would have required an electrical installation certificate from an approved installer.
The cooker control box should be supplied on its own radial circuit direct from the consumer unit. For distances up to 12 metres of run a 4mm conductor cable can be used; any distance over 12 metres needs a 6mm conductor size.
If the cable supplies a cooker only, a 30Amp fuse is sufficient for a 7.2KW load. If the control unit has a combined socket outlet you'll need a 45Amp fuse.
The lights are dimming when the cooker is running because these rules haven't been complied with; your son should get a qualified and local authority approved electrician to make an urgent inspection and report.