Some smaller gears have an increased OD which may explain why you can't find it. Measure the length over 10 teeth of the rack and then divide by 31.42 which should give you the MOD of the rack.

The 3 Colcester squarehead lathes I have owned (early 1970 models) had metric pitch racks ,irespective of them being metric or imperial machines, I dont know when Colchester and Harrison came under one one ownership so there could be a chance that both makers used a common metric rack pitch. The metric rack allows a dial to be fitted to the handwheel to indicate the amount of saddle travel.

That would be 5mm metric circular pitch, though you may get away with 16DP which is very close.

Not just very close – VERY close – half a thou per pitch which is the same as nothing at all for the application. Cut a 12T 16DP gear.

In theory, your 16DP 12T gear should have an OD of 22.23mm plus the long addendum adjustment of 1.98mm to give 24.21mm diameter but they might not have added so much addendum due to it being engaged with a rack I dunno. If you are confident that your OD measurement is correct and hasn't been affected by wear, cut a pinion of that diameter and cut 12 teeth of 16DP into it.

There's a manual here: http://vintagemachinery.org/pubs/detail.aspx?id=18429 and on page 35 (904/2) it shows the pinion as integral with its shaft (so it is a kind of blind gear). That might have influenced the measurement they chose for the OD.

If you can measure the centre distance somehow (pitch line of the rack is halfway up the tooth), that might give some more information to ponder upon. An easy measurement is to go from the shaft centre to the rack tip, just to give you an idea of the absolute maximum root diameter that your gear can be.

Given that you are now faced with the challenge of stopping the new gear rotating on its shaft (key and keyway?) and securing it laterally (space on its inboard side for the projecting head of a fastener), the further from centre you can make the tooth spaces start, the more options you have.

I would also gang up three blanks and cut three gears, then you have spares for the future or in case something gets spoiled.

If this is any help.

When I damaged the rather soft rack gear on my lathe, rather than replace with the "Genuine article". I cut my own 13T 1.5 Module gear, with a short integral shaft. This was Loctited into, and pinned to, the 16 mm Silver Steel shaft. The gear / shaft assembly was located relative to the apron by a brass spacer bush.

Howard