Twiggy,
I am having difficulty answering your question, which sounds so straightforward.
In World War my father was in the Royal Artillery (RA)
He enlisted in Northumberland, and did some service here. But as the RA was country-wide regiment and not just for Northumberland, his records will not be available here in Northumberland.
This will be the same for The Royal Veterinery Corps.
Also the era of service determines where the records might be held. Individual soldiers records for service before 1920 have been deposited in the National Archives
( see their web-site) It is the same one that gives us Census 1901.
Now with the Royal Northumberland Fusiliers, which was a local regiment and was not country-wide, the regimental archives are held locally... in Alnwick I think.
And my view is that there is no advantage being in Northumberland for all those "other" regiments, because anyone would have to go to National Archives in London to search as they are not online.
Michael Dixon