Way, way back controllers could instruct a pilot to use whatever callsign they thought fit if confusion reigned. The obvious one was to ask them to use aircraft registration, which usually solved the problem.
CAP413 suggests that there are constraints on alternative call signs...
An aircraft shall not change its callsign type during a flight. However, where there is a likelihood that confusion may occur because of similar callsigns, an aircraft may be instructed by an air traffic service unit (ATSU) to change the type of its callsign temporarily.
and, if necessary, instruct one or both
aircraft to use alternative or full callsigns while they remain on the frequency.