He doesn't appear on the CWGC listings so he presumably survived the war.
The number was originally issued to the Royal Horse Guards so that would have been his regiment of enlistment but it's a very early number that may relate to pre-war service.
If he's been dead for more than twenty years (I think), then you are allowed to apply for a copy of his service records but it will cost £30 or so and could take up to a year to arrive.
Henk, they are indeed unique and personal but they were re-issued. 304596 comes from a block issued in the 1930s to the RHG.
I discounted a WW1 number as 304596 Allpress is a Rifleman on the Arras memorial.
ALLPRESS, HAROLD OLIVER
Rank:
Rifleman
Service No:
304596
Date of Death:
18/03/1918
Age:
19
Regiment/Service:
London Regiment (London Rifle Brigade)
5th Bn. posted to 1st/28th Bn. London Regiment (Artists' Rifles)
Panel Reference
Bay 9.
Memorial
ARRAS MEMORIAL
I don't understand how the number could've been issued to a chap who died in 1918 and then be used for a Sapper who served prior to 1920 and had a medal entitlement.
You might learn a bit more from the WW1 medal card if you apply for it. Most of the WW1 service records were lost to the Luftwaffe.
I don't think that those two fibre discs are WW1. I'm pretty sure they're WW2.
Have you tried this link?
https://www.forces-war-records.co.uk/NameSearch?FirstName=A&SaveThisSearch=False&RecordType=Ww2&Page=0&RecordsPerPage=0&Surname=Bradbury
When there is A. Bradbury on such a disc I guess it isn't very likely that he had more than one initials like A.G. Bradbury in Dave's link? A.G. Bradbury would fit better in the story but I don't think he is the original owner of these discs?