What current is the spur fused at? Simple answer is add up the power of everything that could be on at one time, then compare it to what you can get from the sockets.

Running a CNC router (so VFD, stepper motors, computer, water pump, maybe air compressor) should be fine on a 13A socket. Mine certainly uses a lot less than that. It's theoretically possible that the VFD could draw 2.2kW whilst the stepper motors are drawing a few hundred watts along with the computer, which might take the total over 3kW, but that's incredibly unlikely - I don't think I've ever drawn the full power from my spindle.
However if you put a kettle or a heater on there that could easily take you over 13A.