It just goes to show that if you're patient enough, all things will eventually happen... Last month I found out that I have some kind of credit history from having my name on DH's credit cards, so next time I was sent an application of my own I sent it in. I didn't think I was going to get it because nothing happened for a few weeks, but then I got an email that my application was being processed - and a few days ago I got a letter saying 'congratulations, you've been approved.' So now I've got a card all of my own and I'll be able to improve my own credit history/score by being good with it.
So you don't have to have an income or independent financial assets or anything like that - you just have to be patient! (we've been married three years and had joint bank accounts for almost the whole time, but we've only got credit cards this year...)
PS. This is a 'real' reputable credit card... no annual fees, no security/guarantees required, no exorbitant interest rates, and a very good limit! So I was delighted to get it...