MNPS regulations apply
(See Edition 9 of the 'North Atlantic MNPS Airspace Operations Manual'). If the failure occured prior to entering Oceanic Airspace (OCA), the aircraft would have to return to an airport per the regulations of the country where the failure occured.
So, if the failure occured within the UK, then UK regulations would apply as to what to do after a radio failure.
Continuation of an Oceanic crossing would be prohibited in this case.
