I've just been refused a credit card although my credit rating is classed as 'good'. Suggestions why?

You should contact whoever you paid for these "credit agreements", whatever they are, and ask them to report this to the 3 major credit reporting bureaus. Any other credit card issuer will still check with Experian and the other 2, and see this on your record. You'll either get denied credit, or offered only high interest cards.

How long ago was it paid off? It's technically supposed to be updated on your credit report the next month whenever there is a change, but that doesn't mean all creditors will do this. You need to contact them about it and complain to a supervisor if necessary. I wouldn't apply for anything else until you know for sure it's been updated. And some credit companies won't give credit, even if a previous account was paid off. Sometimes you just have to wait until it drops off your report completely.

No. You should not apply to any lender for any deal. If you keep applying, that is a negative, and will give them a reason to keep refusing you.

Being refused does not mean that you should apply again, with any lender, for any deal. It means that you should stop applying, immediately, and should not apply for any deal, with any lender, for over a year.

After applying, you should build a record of over a year of not applying before you apply for any deal, with any lender.

If your credit report contains an error, then you need to contest it.