One word - SSN. The Turkish fleet would not venture out of port, it does not have the capacity to mitigate the UK's fleet submarines. So if the Naval option is out they will have to march through Europe and cross the English Channel via the Euro Tunnel? Not sure the Germans and French will go for that?
Turkey may have the second biggest army in NATO, but it has a very limited logistics capacity to sustain an overseas campaign against a foe, which does not border its territory.
Totally irrelevant thread as both parties are members of NATO.
Only conceivable flash point being Cyprus, and if the Turks attempted to take the UK air-base and Intelligence gathering facilities then the conflict would be a Greek/UK vs Turkey affair.