According to lathes.co.uk the motor…
“The spindle was driven by a 440W motor (though the exact power did vary from year to year) and had a speed range from 50 to 3200 rpm”
So like most of these small CNC machines (e.g. Boxford / Denford) it was almost certainly a DC commutator motor, either PM (most likely) or wound-field. Apart from the brushes these motors are pretty bombproof, and replacing the brushes should be easy. However the controller may be a different matter, as it probably used a thyristor or SCR to control the speed and this might have blown. There would also be electrolytic capacitors in it which could be degraded especially if the machine was standing idle for long periods.
So before you rush to replace the motor, have a good look at it – are the brushes OK? If you disconnect it from the speed controller and connect to a low voltage (e.g. 12V) does it run though slowly? Disconnect the controller from the mains and have a look inside, is there evidence of it getting very hot / components browning? Or a “loud brown smell”?
There are a lot of suitable speed controllers around on eBay etc though may not be compatible with the machine controller if that matters to you. Also many of them do not have a speed control input that is mains isolated.