Only the state with whom the aircraft is registered can authorise who can fly it, wherever the flight is to take place in the world. If you wish to fly a UK registered aeroplane using your EASA licence then you must apply to the UK CAA to do so.
I was told you need 2 of 3 things from the following to fly: Aircraft, Licence, Airspace.
You have the airspace and a licence, how do you fly without the third?