Thanks for all your comments. It sounds like there are OK Chinese motors and crap ones, and particularly in view of JohnS's remark:,
' The motors that do suffer are the ones usually fitted to machine that have to fit into a price bracket as the motor is one of the most expensive pieces and it's the easiest one to cut corners on.'
it seems likely that this is a crap one. The machine is certainly built down to a price.
I had hoped that it might be an easy fix, eg bearings, but sounds like it is probably deeper rooted.
I'll try Axminster for a replacement motor, but not got high hopes of getting anything better second time round.
I think I want to keep the machine, so I'll probably be looking for a replacement motor. If I can't find anything British to fit there are plenty of TEC ones on the bay and elswhere which which would fit, and it sounds like they are OK quality (thanks John). With a decent motor I think it'll be a nice enough machine. And OK for for the money even with the cost of a new motor – would have been less happy if I'd paid full price!
Jesse, thanks for your comment – I'm sorry if my original post wasn't clear, I've taken the motor off the machine, and it was the motor alone walking around the bench. The whole machine walking would indeed be scary! My first though was belt / pulleys as well, but there is obviously a problem with the motor.
Thanks again to all for helpful info, Robin