The Safety Reverse version of the single speed tractor was built on the production line as such. It is possible to convert a single speed tractor but you will need the Safety Reverse gearbox which has both dog clutches inside it as well as the forward and reverse gears. As you will know already the single speed tractor has no gearbox at all, just two dog clutches on a countershaft which engage and disengage each wheel.
There is no spare parts listing which covers the Safety Reverse version as it was an optional extra. Operator’s manuals are available in reprint form- try B.J.Sims or Classic Tractor Books.
If you definitely want a reverse gear your best option would be to keep your eyes open for a 3-speed tractor which are more numerous and were produced over a longer timespan.