“Privacy is one of the most important things to get right in relation to this regime.”
David Austen, Chief Executive, BBFC (The Age Verification Regulator)

To verify your age you would have to register in some way with a service that can verify you are over 18. And obviously to do that you will have to provide probably several bits of identifying personal information. That information can then (at least without strong protection) be linked to your porn viewing habits.
The only current protections for privacy are in the government guidance to the regulator which says:

“The process of verifying age for adults should be concerned only with the need to establish that the user is aged 18 or above. The privacy of adult users of pornographic sites should be maintained and the potential for fraud or misuse of personal data should be safeguarded.”

It only takes a moments thought to realise that collection of information about people’s porn viewing habits is going to be very sensitive information. And exposure of that information could be very damaging to someones reputation, relationships and some cases their job.

“For many people – teachers, priests, doctors, to name a few – having your name on a list of adult consumers has real implications.” Vice President of XHamster, Alex Hawkins.

As was seen with the Ashley Madison data leak data, that is particularly sensitive will always be a high target for hackers and those who would seek material for blackmail. And without strong privacy protections that will always be a risk

During the passage of the bill the government seemed quite unresponsive to these concerns:

Alistair Carmichael MP – “Will the data therefore be held in an anonymised form that will not allow the people who have provided them to be identified, should the data be stolen? The best security in the world can still be breached?”

Matt Hancock (Responsible Minister) – “It will be a requirement that the data are held in such a way that they are secure and not made available. It is a common principle across swathes of life that data must be held safely. The Data Protection Act is in place to make sure that that happens.” [Note: nothing said here about data being anonymised]

As discussed separately below, the Data Protection Act has some serious limitations in providing protections in this area.

When the bill was passing through the House of Lords, Lord Paddick proposed an amendment which, in his words would “ensure that the details of those applying to have their age verified in order to access adult material on the internet remain anonymous.”

In the discussion on those amendments he said that:

“In my discussions with the British Board of Film Classification, it has said that it has no particular interest or expertise in the area of data protection in relation to keeping confidential the details of those seeking age verification. We will end up with an age verification regulator that forces users of adult material on the internet to use an age verification solution but has no responsibility for approving such solutions.”

Unfortunately the minister (Lord Ashton), whilst saying “we, too, have absolute desire for anonymity in these matters.” didn’t back the amendment instead relying on guidance to the regulator and saying that “The privacy of adult users of pornographic sites must be maintained. We do not want the regulator to duplicate the role of the Information Commissioner’s Office,”

See here for details of other things that are wrong with Age Verification