I can help with the CDL side of things. First of all you need to get a copy of your credit report so you can see why Barclays rejected you. It could be as simple as a mobile phone contract you took out 4 years ago and missed a few payments on. You can get your credit report from any of the 3 credit reference agencies - Equifax, Experian and Callcredit. You can get a statutory report from these for £2, or you can sign up for their 30 day free trials and be able to view your report whenever you like. I will say that if you go for the free trial make sure you cancel it before it expires otherwise you'll end up paying monthly for a pretty useless service. Also, never pay extra for a credit 'score' - these are generated by the credit reference agencies as an indication of how well you have managed you past credit however they are not used by lenders, who use their own individual criteria to decide if they want to lend to you.
So once you have your credit report, and see exactly what is preventing you from being accepted you'll have a better idea of how to appeal to Barclays. There are a few stories on the CDL thread about people being rejected due to failing the credit check and sucessfully appealing so you might want to take a look there.
Since there are only two banks offering CDL, it's always worth applying to the other choice if you get rejected from the first one. Nobody except the banks really know what the acceptance criteria are, and there are people who get rejected from one but accepted by the other who never really understand why.