More than 1,100 people made the perilous journey across the Channel in small boats on Friday and Saturday, as France accused Britain of failing to provide funds promised to tackle the problem.

After 10 days in which no crossings were possible, 624 people reached the UK on small boats on Friday – the fourth highest daily tally recorded during the current crisis – and 491 did so on Saturday. At lest 40 boats landed over the two days.

On Saturday, after a visit to Dunkirk, the French interior minister, Gerald Darmanin, said “not one euro has been paid” of the GBP55m Britain promised France to help tackle migrant crossings.

The home secretary, Priti Patel, recently threatened to withhold the funding unless more people were stopped from reaching the UK.

But the shadow home secretary, Nick Thomas-Symonds, said Patel’s strategy of not paying up “clearly isn’t working”. He told Sky News: “The home secretary needs to come clean because every single person risking their lives in that dangerous sea crossing of the English Channel is one too many …

“I’ve always thought the home secretary needed to take a different approach. Whilst of course the patrols at the coast preventing people getting out on to the water and risking their lives is hugely important, what I fear the home secretary misses is the fact that nobody becomes a refugee in northern France. We need to be tackling the people smugglers and these vile criminal gangs further away from the coast as well.”

While the nationality and borders bill dictates tougher sentences for people smuggling, it would also mean that anyone entering the UK by an illegal route, such as by a small boat across the Channel, could have their claim ruled as inadmissible, receive a jail sentence of up to four years, have no recourse to public funds and their family members barred from joining them.

The UN refugee agency (UNHRC) has claimed the bill, currently at the committee stage, would violate the 1951 refugee convention.

Since the start of the year, more than 18,000 people have succeeded in reaching the UK on board small boats, according to data compiled by the PA news agency. This is despite the Border Force using pushback tactics that a charity warned on Sunday could have “horrific” consequences.

Kim Bryan, from Channel Rescue, which observes migrants arriving in small boats, said that in the last two weeks, from the cliffs of Dover, her group had spotted Border Force officials deploying pushbacks using jet-skis.

“What they seem to be doing is pushing the boat from the stern and from the bow, and I guess the idea is they’re going to push them back into French waters,” she told BBC Breakfast on Sunday.

Darmanin told Associated Press on Saturday: “For now, not one euro has been paid. We are asking the British to keep their promises of financing because we are holding the border for them.”

But the business secretary, Kwasi Kwarteng, insisted the UK was working “very effectively” with France to tackle migrant crossings of the Channel. He told Sky’s Trevor Phillips On Sunday: “All I can say is that we’ve worked very effectively with the French government so far.”