Usual disclaimer: I'm not an expert, this is just my opinion, etc.

Your credit score means very little... lenders score based on their own criteria, which tend to have more to do with whether you'll make them a profit than whether you're "a good risk". For the record, I'm 29, never earned more than 24k in my life, ongoing debts of 10k and my last known credit score from Experian was 750 - which does suggest that your score is unusually low for your circumstances.You should establish that there are no negative entries on your credit file.

However, the likelihood is that you just don't fit the customer profile that e.g. MBNA is looking for; they want to lend money for profit, after all. Your employee, like me, is borrowing long-term and paying them their interest, which is the sort of market that MBNA caters to. They don't stand to make much out of you.

Unless there is some major problem with your credit file or your address, or your income is really overcommitted in terms of payments, my advice would be apply for a more upmarket credit card (look for cashback, free travel insurance or other perks aimed at the well-to-do), also cards that *don't* cut their competitors throats on balance transfers.

I am unable to recommend a particular card, but Smile (from the Cooperative bank) has been the most generous with my credit limit...so if you want a card with a decent limit for use as a backstop, they might be worth a try. I wouldn't assume that you have a poor credit rating; it is more likely that you don't fit the customer profile.