When some years ago it became clear that they (UK/US-Turkey) would not be able to stop Cyprus from joining the EU some problems became apparent to them:
1)With Turkey occupying a part of an EU member it would be impossible to be accepted, or even given the "date" for EU accession.
2)Turkish Cypriots after seeing the "south" joining the EU they could revolt against the occupation since they would blame Denctash and Turkey for not being able to enjoy what the GC do.
3)If they didn't manage to control this revolution, their strategic interests (bases etc) could be at risk.
They needed a way to prevent the above. Annan plan was their solution.
Accepted or rejected this plan would fit their plans. In either case the result would maintain the fragile situation that is what the Angloamericans want.
Looking back, it seems that they managed to achieve what they wanted:
1)Turkey is promoted as the "good boy" that truly wants a solution, and those bad Greek Cypriots are to blame. Therefore the occupation of Cyprus should not be an obstacle for their EU accession.
2)Turkish Cypriots would now blame the Greek Cypriots for the non-solution and not Turkey. Just to make sure, let TCs remove Denctash also, and put somebody that is seen as progressive and treat this one as their leader. In any case no matter who is the "president" he will not be able to go against the "wishes" of Turkey. And finally, lets give some millions to Turkish Cypriots and a bit of recognition, and why not some hope that soon their illegal state will be recognized. With this, the chapter called "possible revolution by TC" is closed also. This takes care of number 3) and all the friends are happy and satisfied.
Of course, as I said before, their plan was so "perfect" that even if it was accepted they would again win everything. Still, they knew very well that such a plan would not be accepted.
Could we do something to cancel their plans? Maybe we could play it smarter. But this is their game, their rules. If something doesn't work well in their game they can simply change the rules.
There is only one thing we can do, but this is very hard. All those games are played against us based on the fact that we can not trust each other. We don't even trust ourselves to find a good solution.
If we did, then we could find a solution that would serve our interests. And yes, this is our island, and no matter how strong they are, if we were united we could do it.