Downing Street has hit back at a threat by the French president to trigger the customs “backstop” if the UK does not swiftly agree to allow European Union boats to fish in British waters.

The prime minister’s official spokesman said such a threat, if carried out, would amount to a “breach of good faith” under the withdrawal agreement and the UK would immediately refer the situation to independent arbitration.

“If the EU were not willing to engage in a genuine negotiation to replace the backstop with the future relationship or alternative arrangements, for example if it had closed its mind from the outset to the UK position on fisheries, that would put it in breach of its duty of good faith under the agreement, and we can refer this to independent arbitration,” the spokesman said at a briefing for journalists.

On Sunday, Emmanuel Macron had said that unless the UK rapidly agreed to allow EU vessels the same access to British waters as they have now, the talks on a wider trade deal would fail, leaving the UK in the “backstop” customs union envisioned in the withdrawal agreement.

Concerns about the future fishing settlement after the UK leaves the EU have been running high among some Conservative MPs, who are worried Britain will not be able to control its own territorial waters.

Theresa May has repeatedly promised that the UK will be “an independent coastal state”, but the UK will have to reach an agreement with the EU after the end of the transition period in 2020 to negotiate reciprocal access to each other’s waters.

Ministers discussed the state of the Brexit negotiations at a two-hour cabinet meeting on Monday morning, including Britain’s preparedness for no deal amid growing concern that May will not be able to get her Brexit agreement through parliament.

An analysis by the Guardian shows that 89 Conservative MPs have said they would vote against the deal in the Commons. The vote will take place on or around 12 December, at the end of a debate that will be four or five days long.