Mr Barnier, who negotiated Britain’s split from the EU and the future trade agreement, told The Telegraph that the bloc would welcome fresh talks but would not ease its previous red lines.
He said: “It is one thing to say that we can revisit the relationship between the UK and the EU, and in the same spirit we can improve the relationship.
“But it is another thing to say we can open the single market. Any UK government – the current one or the future one – knows the rules of the single market, you cannot be in and out at the same time.”
During his tenure as the EU’s Brexit negotiator between 2016 and 2021, Mr Barnier maintained a tough stance against picking out elements of EU membership without signing up to the necessary obligations.
“If you speak about the chemical sector, you are speaking about a kind of cherry-picking. No way,” he said in a direct blow to Labour’s plans.
However, he said a future Labour government could sign rafts of new EU agreements if it was willing to align with the bloc’s rules in those areas.
“I can speak about defence, foreign policy, cooperation in Africa… financial services,” he said.
“There are a lot of sectors where we can complete trade agreements and open new negotiations between the UK and EU. The main ones are obviously linked to the current situation in Ukraine and Europe with the war, the risk of terrorism, the stability all around us, I think we must, it is in our common interest to open a new negotiation.”
Mr Barnier was more open about the prospect of a deal to reduce checks on British food exports.
“I think there is a room for positive manoeuvre to complete a trade agreement with a specific veterinary agreement to facilitate the flows and exchanges in the sector of animals and vegetables,” he said.
He also highlighted what could become a major challenge for a future Labour government when negotiations need to be held over access for European fishermen to British waters for 2026 and beyond.
“Don’t forget, we have put in the [Brexit trade] treaty the parallel negotiation of the agreement for the UK to access the electricity market of the EU in 2026,” he said.
“We have clearly put these two points in parallel, fisheries on one side with this new negotiation for the access to British and European waters reciprocally, and the access to the UK industry to the European market of electricity. This point has been very clear from day one.
“I recommend both sides to be reasonable at the beginning of this negotiation.”
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