Most sockets are only rated for 10A maximum continuous use in the UK. Even 10A is too much if anything else is running on the same circuit. And that assumes perfect wiring.
Attempting to run beyond this at 13A for extended periods is a huge risk for little benefit.
By far the best option is a dedicated outlet with its own circuit breaker and minimal connections. I appreciate this isn't always an option but it is senseless to take risks.
Often the failure isn't the first time or first ten times you use it, it is a few dozen or hundred times later when the cumulative damage of the thermal stress progressively increases resistance, raises temperatures and results in something burning out. If you are unlucky, it then causes a fire.