What you have there is a lister A type, and its the later twin flywheel version.
A starting handle should be easy enough to find as the starting handle fits on on a 1.1/2" diameter shaft. Which makes life easier, as this is the same size as a host of later Lister and Petter engines use.
If you cannot source one locally, then Stationary Engine Parts in the UK is the next best option, provided you dont mind the fact that this item is not OEM, but is a good copy all the same.