Now that you have given me some more information I can provide some pointers. One thing I cannot do is to link engine and frame numbers with registration numbers except on the very rare occasions (maybe 1 in 5000) where the registration number appears in the Despatch Book. BK5748 / BP8428 went to Andover Motor Cycle Co in Hampshire, leaving the factory on 30 May 1947. Unusually, it had a 4.00 x 18 rear tyre, a 17T engine sprocket and is listed as Competition in the remarks column.
Andover was (and still is) a major British Army base.
LPB 614 is a Surrey registration so a different county from where the bike was despatched to. We can be certain that the bike was specially ordered due to its unusual specification. It was not a bike for the showroom stock. The registration date of 06-06-47 is not unreasonable, although more usually only 2 or 3 days elapse between despatch and registration. 30 May 1947 was a Friday, as was 6th June 1947.
The only surviving Surrey registration records are held by the Kithead Trust in Droitwich Spa. They are primarily interested in HGV registrations so may be unable to assist.
36 4G, 37 VH, 54 KH(A), 75 Healey 1000/4, 52/53 ex ISDT KHA (project).
Former Machine Registrar & Archivist, General Secretary and Single Spares Organiser (over a 25 year period).
Now Archivist once more - but not Machine Registrar.