Raleigh sold their engines to other makers under the Sturmey Archer brand name. Your Rex really has a Raleigh engine fitted to it. It is much easier to find information on Raleighs. The best place to start is the Vintage Motor Cycle Club Library. You can email the Librarian on library@vmcc.net for information.
Meanwhile the following may help,
Ignition advance, max before TDC, 30degrees. Tappet clearance, inlet .004" exhaust .006"
Cheers,