Banks only issue credit cards to people whom they think they can make some money out of; it's not in their interest to issue credit cards to people whom they suspect will always pay their balances off in full, thus never having to pay any interest. So you have no 'value' to a bank in respect of offering you a credit card.
If you're sure that you'll always be paying off your balance in full each month (so that it doesn't matter how outrageous the interest charges are, as you'll never pay them anyway), you can almost certainly get a credit card from one of the companies that specialise in helping people build up a good credit history. Such companies mainly serve the needs of people who've had trouble paying back loans in the past but they can also help 'perfect payers' too, such as yourself.
The biggest players in that market are probably Capital One
https://www.capitalone.co.uk
and Vanquis
https://www.vanquis.co.uk
It's almost impossible to get refused by those two companies!
Also remember that nearly every time you purchase anything on Amazon you're offered it at a lower price (with typically £20 off) if you accept the option to sign up for an Amazon Platinum Mastercard, which (just in case it might ever matter to you) has a much lower interest rate than either of the above. Even if you're not planning on buying anything from Amazon at the moment, you can still get a £20 gift card, just for signing up and, once again, it's highly unlikely that your application would be refused:
Amazon.com User Recommendation
If you're considering
any 'third party' credit card (i.e. one that's not issued by your bank), it's important to check that it doesn't have any annual fee attached to it. (None of the above do).