Is there any risk from plugging in 2 high powered appliances to a double socket? Is the socket rated 13A as a unit or to each outlet? Can it overheat internally?

Even if each outlet is rated 13 amps it is still not good idea to have two items of high rating for long periods of time

Answered by Sarah, Electrical Safety Expert

Even if each outlet is rated 13 amps it is still not good idea to have two items of high rating for long periods of time.

You should monitor the plugs and appliances for overheating and signs of burn. You should check these regularly and allow an electrician to check them every 5 years. 

You can find an electrician local to you here.