You can take as much as you like out but be aware that at both your airports (Dalaman & UK) they have the right to seize it if they believe it has come via illegal means and you can't prove otherwise. I think up to £5k is technically allowed at your UK arrival customs. That's the negative answer, to be honest nobody is going to bat an eyelid over £2k, just get it in larger notes and stick it in your purse.