Not for now. Even if the negotiations finish in the shortest possible time, the UK is still set to implement the GDPR. This means that UK companies also must comply. However, all bets are off in the longer time frame. The Brexit has the potential to affect the application of the GDPR in the UK in the future, though.
Still, even if the UK opts to change the GDPR or abolish it altogether, the privacy regulations in other countries will require a high standard of privacy in the UK. Otherwise, its companies will not be able to hold overseas data.