Charities have criticised a “shameful” lack of safe alternatives for migrants after the number making the life-threatening journey across the Channel in small boats this year surpassed 10,000.

The total includes at least 482 people who succeeded in crossing the Dover strait on Wednesday onboard 21 boats – a record for a single day.

The home secretary, Priti Patel, has vowed to make the crossings “unviable” and the government’s nationality and borders bill would criminalise migrants who attempt illegal routes into the UK rather than entering via settlement schemes. However, humanitarian groups have warned such measures will not solve the problem.

Responding to the latest figure, which stands at more than 10,200 according to PA Media, Tim Naor Hilton, the chief executive of Refugee Action, said: “It’s shameful that 10,000 people have had to risk their lives to reach sanctuary here because the government refuses to open up more routes to safety.

“Ministers must stop wasting time and taxpayers’ money on ridiculous schemes such as fake websites and Facebook pages (deterring migrants) and address the root cause of Channel crossings.”

Despite government rhetoric, the UK continues to have far fewer boat arrivals and asylum claims than many of its European counterparts.

At least 50,989 people have arrived in Europe via the Mediterranean by land and sea so far this year, according to data from the UN refugee agency. At least 1,016 people are estimated to have died or are missing.

Last year, despite a sharp rise in small boat arrivals, asylum applications in Britain fell to 29,456, compared with 93,475 applications made in France and 121,955 in Germany.

Bella Sankey, the director of charity Detention Action, said: “Overall asylum applications are dropping and much lower than they were in the 2000s, but the number of high Channel crossings shows that desperate people trying to save their lives will risk everything to reach safety.

“MPs need to act swiftly and should pass legislation to allow those with strong prospects of receiving protection here safe passage to the UK from northern France to seek asylum here.”

Amnesty International UK said people were putting themselves in “serious danger” because they had no safe alternatives, and urged the UK and French governments to “come together to devise a humane way of fulfilling their responsibility toward these people”.

Last month, the Home Office said the number of police patrolling French beaches would more than double for the second time in a year to prevent small boats from departing, after Patel agreed to pay France GBP55m.

Dan O’Mahoney, the clandestine Channel threat commander for the Home Office, said: “These dangerous small boat crossings, facilitated by criminal gangs, are putting lives at risk.”

He said the numbers were unacceptable and claimed the government’s new plan for immigration was the “only credible long-term plan to fix the broken asylum system”.

Crossings this year – which already exceeded last year’s annual total last month – have resumed in recent days following a period of bad weather. Wednesday’s total surpassed the previous daily high of 430 set on 19 July.