Downing Street has attempted to defuse tensions between British and French fishing industry workers harvesting scallops in the Channel after the French navy said it would intervene to prevent further clashes.

Theresa May’s official spokesman said both sides were hoping for a cordial solution from talks in London on Wednesday designed to resolve the dispute, suggesting there was were no plans for British warships to be deployed.

He said: “The important thing is that there are talks taking place between the two sides. I think everybody – ourselves and the French government – is hoping that this will reach an amicable outcome.”

The French agriculture minister, Stéphane Travert, said on Tuesday the country’s navy was ready to act if there was a repeat of last week’s clashes, when French vessels chased their rivals out of international waters in the Baie de Seine.

About 35 French boats confronted five British craft more than 12 miles off the Normandy coast, with stones thrown and boats rammed in the latest of a series of incidents dubbed “scallop wars”, as they tried to protect stocks of shellfish.

Under EU law, the British are not allowed to fish within 12 miles of the French coast, but smaller boats can dredge for scallops in the 40-mile stretch of international waters known as the Baie de Seine – while the French have access only from November to February.

Travert told French broadcaster CNews: “We can’t keep going on like this, we can’t keep having skirmishes like that. The French navy is ready to step in if more clashes break out, as well as carrying out checks.”

The Department for Environment, Food and Rural Affairs (Defra) said Travert’s comments were in line with the environment secretary, Michael Gove’s position that it was for the French to take any steps needed to prevent violence in the area.

Gove said last week: “These are French waters – it’s the responsibility of the French to ensure that those who have a legal right to fish can continue to fish uninterrupted.”