You're most likely to be accepted if you already have credit, or a mortgage, and have shown yourself to be a reliable payer-back. If you have no credit record when they check you out, then you may find you can only get a card from some of the higher-interest lenders like Capital One. You can however ask Experian or another credit agency yourself for a credit report, I think it still costs about £3 - then you can correct any errors etc before the credit card company look at the report.