I asked this very question on moneybox (radio 4) about 6 months ago...
The girl answered that I should use my parents address...
My response was, well, my parents live abroad, anyway, isnt that a fraudulent claim as I do not effectively live there... she muttered something but concluded if my parents did live in the UK, it would be perfectly alright.
One thing you want to watch, try and get a broker to find the best deal. If you put too many finance requests in, they will label you as a credit junkie and finance will always be refused. Get on your local electoral register as well. Apparently it makes a big difference and you can get the forms online (military form you want). The only other option I do not reccommend is go ahead and say you have lived at the station for 4 years... the whole point about the moving around thing (which could be solved by using NI number or service number in loan applications) is they have a very sketchy finance history on you.
One thing also to note, Credit issuing companies dont like the ammount of disposable income we have. Its bad for their business, especially as we have the means to rapidly pay off debt. In effect your Credit Scoring (no your credit "score" does not actually exist, its an urban myth) tells them the sort of chap you are, and how profitable you are to their financial service. Unscrupulous I know but the way the cookie crumbles. So if you suspect this is the reason credit was rejected (you have a legal right to ask why credit was rejected, and you can then fight your case with them) then remember flying pay is not a salary, its an allowance. Hope that helps!