I've no knowledge of large aircraft operations, but have suffered a complete radio failure in a little aeroplane (and flown non radio anyway on many other occasions).
Standard practice at most UK airfields is to perform a standard overhead join, take a good look at the signal square, and then descend deadside or downwind before continuing the circuit, depending upon which side you find yourself.
I do, by the way, appreciate that this advice is of little use at LHR!
G