Could a stronger British Commonwealth deter an invasion of Cyprus?

Would Turkey invade Cyprus if the island belonged to a much stronger British Commonwealth?

Probably not, because large British naval and air forces on Cyprus would make the operation costly and difficult to sustain.

In this counterfactual, Cyprus belongs to a much stronger British Commonwealth with substantial Royal Navy and Royal Air Force forces based on the island. Turkey could still attempt an invasion, but it would face immediate air and naval opposition. That prospect makes the operation unlikely to begin and difficult to sustain. The military deterrent belongs to the counterfactual Commonwealth scenario rather than a claim about the historical balance of forces.