As by now you will have guessed it is a non-standard thread.
You can get specials made but you will need a mortgage.
If you are competent with a lathe you can screwcut the threads, from time to time 20tpi internal and external chasers appear on eBay and will aid finishing to a good profile. You could even use 1.25mm pitch, (0.050” = 1.27mm), close enough if needs must and particularly if you have a metric lathe. Generally it is easier to do metric threads on an Imperial lathe that English on a metric. I’d be inclined to first make a tap out of silver steel to finish the nuts, (first partially screwcut the threads). Then you can make the studs to fit the new nuts using them as go/no-go gauges, that way if the threads finish a bit off standard who cares as long as they fit? They’ll never see it from the High Street!
Believe it or not, but it is a standard thread or at least it was donkey’s years ago. British Standard Cycle Thread superceded the previous Cycle Engineers Institute threads, and it is a common misconception that all BSC threads are 26TPI. In fact in various sizes above half an inch diameter there is an alternative at 20TPI that was a legacy of the CEI days. I own a superb set of BSC taps and dies and amongst them are a few 20tpi items AND some left hand thread items too that I believe relate to pedal cycle cranks. The wooden case stencil markings suggest that it is an ex-government set from the 1939-1945 era.
Further to my previous comments, please note that the 20tpi cycle thread is NOT of Whitworth thread form. Anyone thinking of screw cutting stuff on the lathe should cut threads with a 60 degree angle and not the 55 degrees of the various whitworth-based threads. For the record, BA threads are also not of Whitworth form. They have a 47.5 degree angle.