Some 254 people were detected in small boats crossing the Channel to the UK on Sunday after an 11-day pause in such journeys.
The figure was confirmed by the Government as more people thought to be migrants were seen being brought in to Dover on Bank Holiday Monday.
There is believed to have been an 11-day break in activity around the Channel from April 20 to 30, when no crossings were recorded amid reports of strong winds and choppy seas.
Following the latest influx , Tim Loughton, a member of the Commons home affairs committee, said while more arrivals could be expected, the Rwanda scheme represented a practical attempt to tackle the problem.
“They are depressing scenes and they are going to get worse,” he told BBC Radio 4’s The World At One programme.
“It may seem a very robust, extreme scheme, but it is the first thing that has actually been put forward that would actually practically do something about this problem.
“People in the south and up and down the country are just sick and tired of these people smugglers making a fortune out of human trafficking, this misery coming across the Channel.
“The Rwanda scheme is an attempt to do something practical about it. But is very early days – it was only announced three weeks ago and it hasn’t started yet.”
On Monday morning, more people believed to be migrants were pictured on the Dover Lifeboat following what was thought to be a small boat incident in the Channel.
The Ministry of Defence took over control of migrant operations last month, when the Government also announced controversial plans to send some of those making the cross-Channel journey to Rwanda.
The Government’s Nationality and Borders Bill – dubbed the anti-refugee Bill by campaigners as it makes it a criminal offence to knowingly arrive in the UK illegally and includes powers to process asylum seekers overseas – became law on Thursday.
Last month, home secretary Priti Patel signed what she described as a “world-first” agreement with Rwanda.
The deal will see the east African nation receive asylum seekers deemed by the UK to be inadmissible, having arrived “illegally” under new immigration rules, but it has been met with criticism and is already facing legal challenges.
Sunday’s figures mean at least 6,947 people have reached the UK since the start of the year after navigating busy shipping lanes from France in small boats.
That is more than three times the amount recorded by this time last year (2,004) and over six times the figure for the same period in 2020 (1,006).
Labour leader Sir Keir Starmer said there needed to be “an international co-ordinated criminal response” to tackle the the “criminal gangs” he said are driving the migrant crisis.
Speaking on the campaign trail in Worthing, West Sussex, he said: “Nobody wants to see anybody making that perilous journey across the Channel and everybody wants to crack down on the criminal gangs that are driving this.
“The best way to do that is to have an international co-ordinated criminal response.”