Start by proving you have a good history when it comes to managing your finances. Having a history of bank accounts (a current account, savings accounts, ISAs, and credit card) will ensure your mortgage adviser has sufficient credit history to look back through.
Despite your best efforts, missing repayments does show that you’re struggling to manage your finances, which doesn’t look good to a lender.
We always recommend not applying for more credit if you’re working on clearing existing debt. Applying for more credit entails a hard credit check, which will temporarily lower your credit score, and you’re likely only adding to your debt.
Holding onto credit cards you no longer use not only poses a fraud threat, but can also be misleading as to how much available credit you have. Make sure you cancel any accounts you don’t use and cut up the card before throwing it away.