is it an eight speed that used to be fitted with a two speed motor? I looked on lathes.co.uk/harrison, but no motor details unfortunately, if it has had a three phase two speed, you want a 1440/2860 (or thereabouts) rpm motor of between2 and 3hp, but if the single phase one is less than this, and you have never managed to stall it,, go for one the same HP as the single phase one. If it was only ever fitted with a single speed motor, it will have been a 1440 rpm one.
Hope this helps, do you have a manual? if not have a look on the Yahoo group for Harrison lathe users to see if they have a PDF, or you could buy one from lathes.co.uk. the pic is the motor in the back of my Colchester, which is a Brooks 3ph, 1.5/3hp 1440/2860 rpm, just to illustrate that they are actually quite small. You would be better off buying a rebuilt or rewound Brook motor or similar than buying a new italian or chinese one! Do you know of a motor rewind shop in your area?
Hope this helps
Phil