Take it logically and trust nothing! Off the cuff:
Is it an RCD or a Circuit Breaker. Can you provide details of what's exactly in the consumer unit
Does an Mains tester illuminate correctly in the workshop on all the sockets? I was thinking one like this
but I see technology has moved on, only slightly more expensive:
Probably not, but could be the wiring to the shed or within it. Does the RCD pop if something else with a beefy motor like a vacuum cleaner is substituted for the lathe? Try several times/ Any other hint of trouble in the shed such as lights flickering etc. Do the lights flicker or dim when the motor first starts to turn?
Is anything else electrical fixed to the lathe such as a machine light? If so remove and disconnect it, and try again.
Just to be sure, is the lathe fitted with a single phase motor or a three-phase motor and VFD?
Probably not, but open up the plug and check the wires inside are OK and on the correct terminal. Follow the wires into the lathe and make sure they connect soundly in the lathe too. Look at all the connections between the switch and motor. Check for damage wherever wires have any opportunity to chafe ot touch the metalwork. If the wiring has been recently replaced, it's possible the insulation was nicked with a knife or damaged during installation.
Is the shed damp or the could the lathe be wet in any way?
If the motor runs completely OK in reverse, and only pops in forward, it suggests the motor is OK, and the fault lies in the switch or in the forward wiring between switch and motor. I agree with Hayden that the switch is the most likely suspect. Reversing switches aren't meant to switch the motor on and off and it can damage them; it may not be rated for UK voltage; or there's debris inside. Not unknown for too-cheap switches to contain bits or for bits to fall off when the switch is operated.
Good hunting!
Dave