Transfers of personal data to non-EU countries are specifically regulated by Chapter 5 of GDPR. After Brexit, Britain is "foreign" as far as the EU is concerned.

It's also worth noting that a lot of Brexiters consider closer political ties and a strong trade deal with the US as an essential element of their ideal Brexit scenario, by weakening Britain's ties to (and dependency on) the EU. In a no deal/hard Brexit scenario, Britain may lack the negotiating leverage to assert any meaningful kind of sovereignty. Many pro-Brexit campaigners have described Britain as being trapped in vassalage to the EU, but a chaotic Brexit could make Britain just as dependent on the US, with everything that implies politically.