The Montreux Convention[0] prohibits large warships from transiting the Bosporous Strait. That carrier displaces 65,000 tons, the upper limit of the treaty only permits warships of 15,000 tons or less. The UK is one of the signatories to that treaty.
Ah yes, it were two ships part of the Queen Elizabeth strike group, but not the carrier itself. The command was given by the admiral that was on board the Elizabeth.
Now that you write that it makes sense why they would send only two ships and not move the group around there.
0 - https://en.wikipedia.org/wiki/Montreux_Convention_Regarding_...
1 - https://en.wikipedia.org/wiki/Queen_Elizabeth-class_aircraft...