TOPIC:

Can anyone tell me if the army number allocated to a soldier in the Boer
War would continue to . Their First World War regiment would give them a new number or not?

4015 was William Cooper's number but I am having difficulty searching and finding his details for WW1 records,

The number could continue, although, certainly not in every case, a brief look at available service paper folios shows two men with this name and number, one in the Cavalry, the 6th Dragoons and another in the Militia, the 4th Bedford's.

I have just noted your other post of some two weeks ago and I am a little confused, you say that you have been "given" his number etc, how do you know this is the man you are looking for, why do you believe he served in the Anglo Boer War and the Great War and why do you think this man is William John Cooper, I would suggest he is not.
On the subject of numbers, men who joined the Militia did not serve in it during the Great War as it had in effect ceased to exist, it had actually become the Special Reserve upon formation of the Territorial Force.
Regarding the actual man you are looking for, do you actually know his date and place of birth?
William John Cooper is a common name and it would be a simple case of going through WO363 and looking at all of them, but, obviously quite pointless if all you know is his name.

Thank you for you interest. William JohnCooper was my great Uncle and his G/daughter has given me the details. He joined up in 1899 initially in the Reserves? He was born in 1881 in Poplar , London. Looking at some records I have managed to find he was in the Boer War the. Obviously transferred at some time during 1912 and joined up again for the WW1. I have seen several W J Cooper's during my search and yes it is a common name but I have always looked for the match of his 4015 number. He was awarded several medals from Boer War so I am sure I have the correct info. I believe he left the army as a Warrant Officer.

Okay, well in that case you can forget about 4015 William Cooper 4th Bedford's Militia, very clearly, he is not the man you are looking for!
The obvious thing to do is have a look at the naming on the medals you mention.