I think the problem is going to be that the UK does not recognise TRNC and so is unlikely to accept monies from there, however I would assume that the bank itself is a Turkish bank and so the monies would be routed through them. As per the best bet is going to be asking the sending bank.
If you need to regularly transfer money from the UK it is best to find a bank that makes that transaction easy because a cheque can take one month to clear.
Go into your bank and tell them that you wish to make an overseas Electronic Funds Transfer. Fees could be around £25 mark depending on how much you send.