How to get a first time credit card?

UK.

I've never had a credit card before. I'd like one just so that I can build credit history and make my life easier in the future. I'm 23. I've got a steady income and no credit history at all. I've never owed money and I've never come close to having nothing in my bank. I've got over £10k in my savings account.

I tried applying for one today, however it was rejected at the soft check. I figure it's probably because I have no credit history. I've looked on comparison sites and none of them can find me a credit card that I would be eligible for.

I asked my bank for any options I have to try to improve my chances of getting a credit card, however the customer support couldn't give me anything they deemed as financial support. All they did was tell me that paying off an overdraft improves credit scores, however I somehow feel doubtful that will be enough.

But what do I know? Honestly to me the whole thing makes my head spin.

I can't seem to get my head around the logic that spending more than I have and then paying it off is better than never spending more than I have and having a lot of money saved up. It just doesn't click with me and I would consider myself a pretty smart person.

So I'm going to look up on getting an overdraft now.

It leaves me wondering, how do I get credit history if I can't even get a credit card?

Or as the big question above says, how can I get my first time credit card?

Any help is greatly appreciated thank you.