Credit card debt is classed as a non-priority debt. Although non-payment will usually only result in a minor consequences, some non-priority creditors can still enforce bankruptcy and issue county court judgements.
If you are up to your limit, and unable to meet the monthly payments, write to the credit card company and explain the situation. Make it clear you are not going to use the card again, offer a monthly repayment scheme, and ask them to freeze the interest on the account. Send in a copy of your financial statement to provide evidence of exactly how much you can afford, which will make it much more likely for them to accept your proposal.