Okay, I feel dumb but I just now noticed that you're in Scotland.
I don't know how many staghounds might be in the UK, at least the kind we have over here in the states. Your guy is probably what folks over there would call a lurcher, a sighthound mixed with something else. People breed them as hunting dogs, mainly because in the old days it was against the law for "common people" to own a purebred wolfhound, greyhound, etc. since it was illegal for common folks to hunt. The gypsies would steal greys and breed them with collies, terriers, whatever they thought would make a good cross so that they could have a hunting dog for poaching and not be executed for it.
As far as I know, different breed crosses are made for different purposes, like whippet X terrier, greyhound X collie, greyhound X saluki, etc. Here are some links to lurcher organizations in the UK. Seamus (our dog) has the build of a greyhound bearded collie cross, but I don't think that's what he is because of the wire hair. You might try contacting some of these folks, they'll probably have a good idea of what breeds were used to make your dog.
(this is slow site! be warned)
Keep us updated with him! Lurchers are great dogs all around.