If you have his army medals his service number should be engraved around the rim, if he married whilst serving in the army or if any of his children were born during his active service his regiment and service number may well be on their certificates or the marriage certificate.
It will not be too easy unless you know the regiment, maybe if you find out which town he enlisted in that would give u a clue, was he called up, was he regukar army, do you know the job he did? If he was from the North East there are certain regiments associated with the North and Borders i believe.
Dotty