No it won't. Unless you ban EU citizens visiting your website and your website doesn't make business with other businesses in EU.
>Britain will attempt to move away from European data protection regulations as it overhauls its privacy rules after Brexit, the government has announced.
Other countries like Canada implemented GDPR directive. EU required this from Canada, Japan and other countries to make some custom/tariff -free deals. Looks like UK wants to break away from dealing with EU at all?