The US Logan Act is a law that criminalizes negotiation by unauthorized individuals with foreign governments having a dispute with the United States. I believe the UK should have something equivalent as the EU is essentially a foreign government with whom the UK is in current dispute.
You may be interested in these active petitions
Had the UK an equivalent of the Logan Act, there would unlikely been so many British individuals, who have never accepted the 2016 EU Referendum result and have worked ever since then to undermine its effective implementation, in discussions with the higher echelons of the EU in Brussels and key Member States' leadership of the EU 27.