It could have been done anywhere. Armourers were renumbering weapons all the time - with the same number of course but where they were illegible or indistinct. Fazakerley were the worst offenders with their barely cutting engraving machines or 'scratchy pens'
If we could just about read the numnber, then all well and good but if it was illegioble, then we could usually find it from the unit 'WOCS' register (that's War Office Controlled Stores register) If you didn't have a clue what it was and couldn't 'cook the books' so to speak......., not that an Armourer ever would you understand, not even rushed off his feet with work up to his armpits, then there was a system whereby a new number could be allocated from a specially reserved block of numbers
Has that answered the question in a roundabout way?