As John says, There is an argument for not necessarily jumping into buying another motor.
That said, if that’s all that is problematic about the lathe and it is going up for sale, nothing slashes the desirability of an item like a core part of it non-functional.
John definitely makes a good point about someone wanting to stick a 3 phase motor + VFD on it (although to be fair to the 7 series lathes, their belt changes are about the most convenient on any similar sized lathe, if it’s convenience that’s driving the change from 1 ph to 3 ph), but even someone intending to change out the motor is going to expect a significant markdown on the price.
If you want to sell it with a working motor, maybe an idea would be to preempt the desire to have variable speed, by installing a 3 phase motor and include a cheap VFD.
https://inverterdrive.com/group/Motors-AC/ac-Motor-550W-550-Watts-4-pole-B3-71-TEC-IE3
and
https://inverterdrive.com/group/AC-Inverter-Drives-230V/WEG-CFW100C04P2S220G2
Okay, yes, that’s about £188, so not strictly speaking £100-ish, but the ‘infinitely’ variable speed almost ‘out of the box’ for the buyer, could be quite a draw.
If you just want single phase, then I reckon take look on eBay for used (don’t bother trying to filter by anything other than “single phase” and “induction”, half the sellers don’t seem to know what it is they’re selling, and the variability of the description including HP or Wattage to describe the power, never mind including the number of poles, means you just have to trawl through the listings), or probably more sensibly just use @Diogenes link, as that’s a pretty good deal for a single phase 3/4 HP (0.55KW) 4 pole motor.