Extention to wiring

The wiring on my new airing cupboard dual towel radiator does not reach the cupboard socket. Would it be safe to add a connection joint to an additional length of same type of wire with a 5amp plug. I note it stressess that it must be earthed. I take that to mean that the earth wire is also connected to the inside of plug.

 

The problem is that it is a single socket and being as such I could not see this being an option. I thought an extra 18 inches of correct wire attached via a good connection to the wiring of the duel towel radiator (water in winter switch to electric element in rad in summer) should resolve the situation unless I am overlooking something.