JennyCee
I have an account with a well known Building Society and have applied twice for a credit card. The first time for use in Australia when I went to visit my daughter and the second because I just wanted one for safety online. I also have a very healthy balance but both times they have refused me. They wouldn't tell me why. Apparently they don't have to.
JennyCee It is nothing to do with how much money you have in the bank, all about whether the bank think you will use your credit card frequently enough to generate enough income for the bank from the companies you will deal with.
Banks are commercial companies who need to make a profit. If you are only going to, for example, spend £200 a month on your card, generating roughly £6 commission for the bank, and the adminstration of a card costs the bank £10 a month, then they will refuse you a card because it would cost them money.
Remember you do not have to get a credit card from your bank. Tere are hundreds of reputable credit cards available. For the last 40 years plus, I have quite deliberately never had a credit card issued by my bank.
You can also do a credit check with one of the credit card agencies, and you may find that your problem is that you have no credit history. You have not borrowed money over the last 10 years, your use of any credit card has been minimal, so that the bank have nothing to judge your creditworthiness on, so do not want to risk giving you credit.