A total of 513 people reached the UK after taking the dangerous route in 15 small boats on Saturday and Sunday, the vast majority of which were taken to the coast in Dover. The numbers have continued to rise despite the government unveiling its Rwanda asylum partnership earlier this year, which deports illegal immigrants arriving in the UK to the African country.
Ministers hoped the plan would deter people from crossing the Channel to reach Britain.
However, flights to remove those here without justification have yet to begin after the European Court of Human Rights intervened in June to block the take-off of the first plane.
There are concerns that the number of people making the crossing will continue to rise until the policy is fully operational.
Ministers say people smugglers are exploiting the current pause in the policy to convince vulnerable people they have only weeks to reach England before the route is closed.
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The figures suggest the UK will soon surpass the total of 3,053 people rescued by August 2021.
MPs are concerned that vulnerable people could die if they try to make the crossing.
Additional concern has arisen after at least 27 people died in November last year after their dinghy sank while trying to reach the UK.
Both Mr Sunak and Ms Truss have vowed to see through Rwanda policy if they become conservative leaders.
The former chancellor said he would “do everything” to get Rwanda’s plan “off the ground and working on a large scale”.
The foreign minister, who outlined her position last week, said she would “support and expand” the scheme “to more countries”.
“We have to make sure that the terrible people smugglers fail to bring small boats across the English Channel,” she said.
“I would support Rwanda’s policy and expand it to more countries, but I would also make sure that we cannot be overruled by the ECHR in UK law so that we can protect our borders.”