Saying "we don't know" is like saying you believe in Father Xmas...However, I can't prove there isn't one, but...
At least I admit that I don't know, whilst you seem to be convinced you know the likely course history would have taken.
Cyprus, because of it's history required a far more complex independance than many other colonised nations, the communities were polarised anyway, if the British had just upped and left (but they wouldn't, as they wanted the bases) it's fair to say that either a bitter civil war would have broken out, followed by Greece and Turkey becoming involved, or Greece and Turkey would have just gone straight to war anyway.
OK, leaving the British out (which was the original premise), we know that Cyprus would have been part of the Ottoman empire. Come the Balkan Wars, followed by the 1st World War, what do you think the chances of Cyprus staying intact would be. Let's add on to that the Greek-Turkish war immediately after the 1st World War.
At this point, Cyprus would have been treated in the same way as all the other contentious land negotiated over in 1923 when the Treaty of Lausanne was signed. Greece at this stage were on the back foot, and Turkey had already begun expelling all the christians in her territories.
At this point Greece had already expelled muslims and would more than likely have carried on as Turkey progressed with her expulsion of christians.
The exchange of populations agreed by Greece and Turkey at this time had the key objective of creating two religiously and culturally homegenous nations. In other words they wanted as few people of the other religion and culture as possible in order to promote this concept. To this day both countries are still extremely homogenous. What are the chances then that at that time, had Cyprus been in the mix (which it would assuming Britain had never gotten involved), that Turkey would have insisted on keeping its minority of TCs and oust the GCs whilst it knew it would have to allow even more Greeks to stay in the regions that mattered to it most (those around Istanbul which were full of Greeks)?
Again, I don't claim this is a dead cert, but to say it is very unlikely is quite wrong. Turkey was on the back foot after both World Wars, and Greece, if you like, backed the right side. I think it's more than likely she would have annexed Cyprus at some stage with the allies blessing had Britain never set foot in Cyprus.
Going back to the assumption that Britain gives Cyprus independence in 1950. There is still a chance that civil war would break out but at least it would not have been preceeded by a 6 year guerilla war in which GCs are pitched against TCs and the two communities ideals of Enosis and Taksim are allowed to gather momentum. Again you cannot seriously turn round and say that it was almost guaranteed that an independent Cyprus would not work. What was more likely at this time was an ideological war between Communists and Capitalists which had happened in both Greece and Turkey around this time. I agree that the communities were already polarised but at this time both Greece and Turkey were receiving Marshall aid from the US and it would have been in the US' interests to keep things sweet between the two, at least until the communists were dealt with.
The Aegean islands were not a threat to Turkey in 1923 as Cyprus could have been in 1974 with the advent of missiles and planes, look how Turkey was prepared to go to war in '97 over the possible installaion of the Russian ant-aircraft missiles.
Yes, ok, but I thought we were talking with the assumption that Britain never sets foot in Cyprus in which case Cyprus would have been dealt with in 1923 (in all likelihood). At that point Cyprus would not have been considered a threat, and the chances are many of the TCs would have left or been forced to leave in 1923 under the treaties terms (as was the case in Crete). Perhaps Tuirkey would later find problems with Cyprus, as she has with the Aegean islands on which Greece has military outposts.
We still don't know, I am just saying it's just as wrong to think that Britain gave GCs the chance of self-determination when they didn't have one as it is for GCs to pile the blame for their problems on Britain.