From 'British Forces Motorcycles' by Orchard and Madden. Contract S6287 was for 3500 machines (reduced to 2000 in May 1945). Frame numbers XG51856-XG55355. Ron
email (option): ronpier@talk21.com
The contract itself starts from a specific engine and frame number..
Once you have those numbers (found within the records of the contract) it's a simple case of comparing your own machines numbers to the record to establish where in the contract it was produced...
There are various preserved/published records that contain what's needed for the majority of contracts...Ian
email (option): ian@wright52.plus.com
Well I calculate yours to be the 258th bike in that contract with census number C4589683. Your engine is from two contracts later in the same period (demanded in 41 and completed in 42).
Armed with this imformation, I guess you will be rushing out to the shed to flat down the shiny paint for a coat of service brown
Ron
email (option): ronpier@talk21.com
Generally speaking, the frame numbers run in sequence to the census numbers. You simply subtract the first frame number in your contract from your frame number then add to that number the first number from the census numbers.
For example in the case of your bike. XG20758 - 20501 = 257 + 4589426 = C4589683. This is the easy formula to determine a C number, but of course as you've used the first frame number to deduct from yours, you must add it back to know that your bike was the 258th bike off the assembly line.
It can also gets more difficult with split contracts (like yours) that were issued multiple sets of census numbers.....Often it can be a 'best guess'.
I numbered one of my Velo's using this formula, only to find out years later from the VOC who have copies of the factory ledgers that Velocette didn't follow the procedure to the letter and I'm 60 out with my number 
I'll correct it if I ever need to respay my tank. Ron
email (option): ronpier@talk21.com
That is very rarely possible I'm afraid Richard. We would all love to know where our bikes served and who with 
Sometimes the only possible way to have a clue is if by some lucky chance you could find some original markings (maybe under layers of paint) and not put there by a previous owner.
The records that we have available to us, will usually indicate that a motorcycle was supplied to either the Army, RN or RAF but not to any specific unit.
I do have a Velo that is from a batch that was initially ordered by the French government, but as Paris had fallen before they were dispatched, they were reallocated to other British units. Fortunately the VOC have the records for these bikes and mine was sent to an anti aircraft unit in Lincoln. This is the only bike in my collection that I actually know what Army unit it served with. I also have a Royal Enfield that I know was supplied to the Admiralty at Chatham Docks. Ron
email (option): ronpier@talk21.com
my wife found one at a bookshop in Hastings? just waiting for it to arrive 
kind regards
email (option): woolnough@mchenry.plus.com