Way ahead looks clear to me: Nigel says the capacitor on his Burgess is marked 4µF, and John Haine provided a link to suitable 4µF motor run capacitor on RS, cost £4.51. No need for guess work in Laurence's case!
Assuming Nigel hadn't been able to confirm 4µF, how could the size of a run capacitor be found? Replacement run capacitors available between 2 and 40µF and what's needed doesn't seem to be related to anything obvious like HP. My guess, inductance of the winding, which is a consequence of the amp/turns needed to produce a suitable magnetic field.
There is so much I don't know! What is it about a motor that decides start and run capacity, and is it possible to establish the size with a measurement? (In my youth Inductance meters were expensive Lab tools, today ebay is your friend!)
Dave