It wasn't a fear of taking over outright, it was a fear of taking over as a sphere of influence. Crete was unified with Greece since the Treaty of London 1913. The question with Churchill was whether or not Crete would be in the Russian, or British sphere of influence (SOI). For Russia, it was important to have Greece on their side as it would prove them with an outlet from the Black Sea, through the Sea of Marmara, into the Mediterranean. For Britain, it was imperative to maintain control of those seas. By WWII this had come to mean shipping canals, primarily, the Suez Canal, and Britain was not willing to let that go (obviously).

Now in terms of the 19th century and the Ottoman Empire. No. Russia had no such intent. Serbia was the first to declare themselves independent in 1804, to settle in 1815, Greece was second in 1830.

Constantinople was not threatened much until the Greco-Turkish Wars 1919-1922 and Greece was forced to give in under British pressure.

The British, French and Italians withdrew support for the Greeks in 1922. Britain was first, France and Italy second. Soon the Greeks lost support from the West for everything, had to abandon the conquest of Constantinople, and abandon Smyrna.

Britain sent troops to Greece to defend against the Nazis in WWII to no avail, after that, Greece succumbed to civil war, where Yugoslav Communists supported Greek Communists to obtain rule from the Royalist government Britain supported alongside the USA (the Truman Doctrine),