Hi djc,
the nameplate also shows that it is an Excel lathe made in Coventry in the UK (the original poster is UK based so it is more than likely that it is an actual Ecxel lathe as described here:
http://www.lathes.co.uk/excel/
However the saddle and cross slide look a lot like the ones Emco used on their larger lathes such as the Maximat V10 etc. The guy at Lathes.co.uk has some spares so he may be able to help. It would help if we could have accurate measurements with a micrometer or vernier caliper and as you say, the pitch, if he can't manage that perhaps a photo of the broken nut alongside a metal engineers rule would help.
TerryD
Sorry, but the "name plate" is a sellers name plate, at least the Jet name plate had the Made In China legend in very small letters. That sucker is one of the generic 9X20 Chinese lathes. I know, it's a 918 in this case. But 920 is sort of the generic term for these machines, the Jet branded machine was a BD920N.
They are or have been sold by many different companies, although supplies seem to have dried up with recent events. In North America Jet, Enco, Grizzly, at one time Harbor Freight, I think Princess Auto, most of the catalog machine tool outfits, and just about every other tool importer has sold or still sells this model. The good thing is that being so common most importers MAY have replacement parts. I owned one of these machines for around 15 years, and own a Compact 5 CNC which I'm retrofitting to modern controls, so I have up close hands on knowledge of both machines.
Here's one version offered in the US.
https://www.grizzly.com/products/grizzly-9-x-19-bench-lathe/g4000
The PRC 920 lathes are not in any way related to any of the higher quality machines other than general layout and dimensions. If anything, they take their design and manufacturing compromises from the lower cost Atlas lathes sold in the mid 1900's by several large retailers in the US.
The Chinese 920 models sold in the US typically (always?) have metric leadscrews and imperial dials, so you always miss dimensions on any good sized cut if you trust the dials. Replacing ALL the hardware with good stuff and adding a stiffening clamp down plate to the compound pillar is almost required before you can use the machine to it's fullest capability. I did some good work on mine, was glad to have it rather than no lathe, but am glad to have a different machine today.
A search on fixing and upgrading 9X20 lathes will likely turn up many options for sorting out some of the issues with these lathes.
In spite of shipping costs, it may be easiest to see if Grizzly has a replacement part available, they are a firm that has made at least a good effort to stock spares for the machines they sell. Odds are UK machine importers may have parts as well, just not folks I have any knowledge about. Shipping on one of your kits to the US wasn't unreasonable, don't know if that's true going the other way though...
I sort of recall that my cross slide screw was just a normal V thread with 1mm pitch, although I don't remember if the diameter matches any available taps. The cross feed dial was graduated to indicate 40 thou per turn, but a dial indicator would tell you a single turn was in fact 39.4 thousands of an inch.
If in a real bind, remember that you can lock the cross slide in place using the gib and gib screws, and control depth of cut with the compound. Everything else still works OK I think? This would allow you to fabricate a tap fairly easily using silver steel / drill rod. If you use it to open up an acetyl replacement you won't need to even harden it, and unhardened it would probably work fine for a single use in brass or aluminum. Don't be hesitant to give it a try, taps for limited use in normal V thread form are easy to make, I've made dozens of oddball taps over the years, after making the first one I had to wonder why I'd been so hesitant to try
Best of luck sorting it all out,
Stan