First the UK side of things needs to be sorted, the executor has a legal duty to correspond with the benefactors of the estate, if they refuse then they can be held accountable under British law for that and its a serious matter to breach the duty of being an executor. This needs to be done by the benefactor.
The Turkish courts will consider a UK will although they are not bound by law to accept it if it is breach of their civil code. This was as much of a concession as could be wrung out of them by the consulate who announced it on their website some time ago. Either way, the unreserved portion of the estate does belong to the deceased person's partner, it is only the minority share at best that the relatives can claim.
Things have moved on a lot in Turkey since this sad business started, one dear late forum member's relatives were asked to provide proof that the deceased had not had more than two children (this was two years or so ago now) and as this is obviously a very difficult thing to prove the consulate stepped in and sorted things out.
I would suggest sorting this in the UK first and then re-present the will to the court in Turkey. The relatives who wish to challenge the will should have made their case to the court a very long time ago and chances are they haven't.
Karyn