No, the Age Verification system (recently delayed[1]) is compulsory that porn sites must implement to be able to trade in the UK. It requires that they perform age verification on everyone accessing the site from the UK. This verification would be performed by supplying ID and linking it to your account.

This is separate from ISP supplied filters in that it applies to the porn companies themselves, not the end consumers. Obviously a company like Mind Geek having your ID and all your porn browsing history is not worrisome at all.

1: https://www.ispreview.co.uk/index.php/2018/03/age-verificati...