I'm probably one of the few here with a workshop full of 3-phase stuff, so....
What you need to know is the size (kW) and speed (rpm) of the existing motor and you need to take a look at the motor mounting plate - is the motor mounted conventionally on feet? 3000 rpm will mean a 2-pole motor,m 1500 rpm a 4-pole motor (more expensive). I'd be careful about taking on a 16in P/T as you are probably looking at 5 to 7HP (see note below)
There are 2 main ways to convert a 3-phase lathe to single phase:
1. Swap the 3-phase motor for a single one. May require a replacement pulley, too and the DoL starter might not be big enough either (a 3hp 3-phase 415volt motor requires 1a 6Amp contactor set, 3hp 1-phase 240volt requires 10amps), or the coil could be a 415volt (phase to phase) coil which is no good for 240volt operation. Contactor sets come in from £20 to £30, motors 2 to 3HP run £70 to £100. Try Machine Mart for both.
2. Install a static phase inverter. This will convert single phase to 3-phase. Costs on 2 to 3hp in the region of £150 to £250 if you eBay it. If you are lucky you might pick-up one which will allow frequency regulation -0 so you can change speed by changing the frequency of the current supplied to the motor. This is more expensive, but MUCH simpler.
Remember that on start-up a 3hp motor potentially draws 16Amps - more than a 13Amp plug can take so bigger machines need to be connected through something like a BS.4343 plug or permanently wired through an isolator box. Make sure that the circuit is protected by a motor-rated (type D?) MCB and NOT a fuse. Avoid anything boigger than 3hp as you'll have the devil of a time getting a motor and wiring it in (the greater amperages onb 240volts will require heavier wiring)
Lastly, are you sure that you can manhandle these items into your shop? Cast iron weighs a heck of a lot (that lathe will be potentially 1/2-tonne plus, 1-tonne plus if it's a big Wadkin or Pickles) and getting it down a gravel drive isn't an easy option.
As you're also in W. Yorks if you'd like some more info, why not PM me?
Hope that helps
Scrit
Mods - any chance of generating a FAQ or something for this?