Earlier quoted context omitted.
People already make accounts with phone numbers, I suspect credit cards won't be different.
The number of active credit card holders in the UK is somewhere in the 35 million range. The number of adults is somewhere over 56 million. There is quite a mismatch there. Unlike the US, owning a credit card is not standard for most people in the world. People tend to get them for online shopping abroad, and for travels out of their currency zone as a back up.
If you can login to your government tax account, or apply for a DBS, you'll be able to prove your identity.