Conservative MPs have urged Priti Patel to immediately send back anyone who joins an illegal crossing of the Channel from France, including children.

They claimed the measure should be enacted because the UK needed to “up the stakes” with the French government, which has been blamed by the home secretary for failing to curb the number of migrants sailing across the channel.

The suggestion, made a day after more than 800 migrants crossed the Channel to seek refuge in the UK, has prompted a furious reaction from Paris.

An interior ministry statement warned the UK not to attempt any action that is contrary to international law, which it said would result in a “serious loss” of confidence and cooperation.

“We also call on the British government to be cautious about the announced use of procedures to fight against attempted sea crossings which would not only be dangerous for men, women and children onboard these boats, but contrary to international law,” the statement said.

“If the British government were to choose another path, we will draw our own conclusions.”

Patel, under pressure from Boris Johnson and senior Tories to stop the flow from Calais, told MPs on Monday she was ready to withhold £54m promised to the French to block migrant crossings.

Craig Mackinlay, the MP for South Thanet, said that sending back all people who arrived in boats, including children, would be a “high-octane measure”.

“Immediate relief is in the hands of the French authorities. We need to up the stakes and consider immediate removal back to France of all who arrive via this illegal route and disregard diplomatic niceties.

“This, above all else, would show, and rapidly, that the route does not work and the migrants would simply not waste their money in trying it.

“I know that the home secretary is as frustrated as many of us and I have recommended such a high octane measure to her,” he said.

Lee Anderson, the Tory MP for Ashfield, said he made the same suggestion to Patel at a meeting in central London on Monday night and knew of other MPs who agreed.

“I said we should drop these illegal immigrants, not migrants, off on a French beach and send the French government a bill for the cost of the journey,” he said.

A third Conservative MP, the member for Dover, Natalie Elphicke, wrote on Twitter that she supported forcing boats back to France. “If the French won’t stop the small boats then we need to,” she said.

The proposal to send boats back was condemned by Pierre-Henri Dumont, France’s MP for Calais, who said it would be a blatant breach of human rights laws and an insult to the dignity of those seeking asylum.

“Not giving a chance to children to be protected is something that should be tolerated in modern society. We are talking about human rights and dignity.

“This suggestion tears apart the UN Geneva convention giving the right to everyone to apply to any country for asylum.

“The UK left the EU but the UK did not leave the international community and the UN,” he said.

The UK is a party to the UN’s 1951 convention relating to the status of refugees and to its 1967 protocol, a piece of international law designed to protect refugees.

A Home Office source said the MPs’ suggestion may not be workable without a change in the law. The source said the nationality and borders bill, which is moving through parliament, contains provisions to set up offshore processing centres and turn suspected migrant boats away from the UK.

Mackinlay and Anderson’s comments follow Patel’s decision to blame the French authorities for the record rise in the number of migrants. Patel threatened to withhold the money, promised in July, at a meeting with concerned MPs.

The Home Office has yet to confirm the final number of migrants who crossed the Channel on Monday. Government sources said it was likely to be between 800 and 850. The previous daily record was set on 21 August , when 828 people crossed.

Labour criticised Patel’s claim that she would withhold money and urged the government to stop chasing headlines and instead form a working relationship with France.

Nick Thomas-Symonds, the shadow home secretary, said: “The government should be focusing on finding a workable solution with the French authorities, tackling vile people-smuggling gangs and properly managing safe routes to prevent people risking their lives.

“It is about time solutions are found, not another headline.”