If they want a full access to the EU market they will have to use the EU regulations like Norway does. However they may prefer a hard brexit for some reasons.

The GDPR regulation is implemented into British law as the Data Protection Act 2018 [1]. It must remain until the end of the year. If there's "no deal" then, next year, the UK Parliament may repeal or modify it as it wishes.

However, there were data protection acts in 1998 and 1984, and it seems unlikely the general principle of access to personal data -- which was there before GDPR -- would be removed.

[1] https://en.wikipedia.org/wiki/Data_Protection_Act_2018

It probably won't if Big Tech gets its way with government. Remember, GDPR isn't in their best interests.

Brexit allows them to start again on that side of the Atlantic, albeit on a smaller scale.