To answer Electrochem's point, Bob....
Of course it's a good idea to have an electrician carry out this kind of work, but Building Control don't necessarily have to be notified.
New circuits are notifiable, but if this is just an extension to an existing circuit, it's not necessary unless it's somewhere such as a bathroom.
I agree with Electro. I wouldn't have done it that way.
Could you tell me what you mean by 1/2 armoured cable, Bob?
Also, is the circuit protected by an RCD actually in the house, as well as the one in the shed?
As for warming. Normal for high loads such as 3kw. Or even smaller loads for extended periods.
Loose wiring connections can do this.
Even loose contacts within the socket. (Where the pins go in.)