Jamie, beware that applying for credit actually reduces your credit score, and getting turned down seriously reduces it - so before applying for another card, it is worth spending £1 getting your credit report off the parasites who peddle your personal information for corporate profit and seeing what shite they're putting out about you - more often than not it is wrong!! - by blindly applying for more credit without knowing exactly what the 'problem' is, you risk screwing your credit record up for years.
These companies should be banned full stop. Should go back to the good ol' days of personal relationships with a branch bank manager who you could talk to and (try) to reason with. Now it is just "computer says NO!" and they won't tell you WHY unless you give them money for the privilege of getting YOUR OWN private information! Blackmail. Basically.
Credit reference agencies are a total con, I am sure they deliberately muck up people's credit scores to trick you into paying a fortune for a "credit health check", just so you can make sure they have got YOUR personal information correct - information that they should never have in the first place. Parasitic scum, the lot of them. I for one will NEVER play their games again... Learnt my lesson the hard way.
Earn, save, pay in cash, and screw the *system* they try and force you into for nothing but their own commercial gain! You can exist quite happily without any credit, and thus defeat them. OK, buying a house cash is perhaps not realistic, but when you realise what the word "mortgage" actually means MORT=death, GAGE=grip - you begin to wonder if you want to be in the DEATHGRIP of a banker for almost all of your working life just to say you "own" your house - which of course you don't own anyway until a few years before you die (if you're lucky!) - the banker owns your house, and holds a DEATHGRIP over you where he can snatch it back anytime you stop coughing up the £1m that you must pay him for the house you are led to believe you own that *only * cost you £250k.
/rant over
...ignore my rant - but seriously, be very careful about applying for any more credit before knowing why you were turned down this time.