'Infinite' numbers of migrants hope to illegally enter the UK ministers fear, with the Government privately conceding their deal with Albania will not end the small-boats crisis.
Whitehall insiders believe even if their agreement to return those arriving from Tirana is successful, there are huge swathes of migrants from other countries ready to replace them
More than 45,000 people crossed the English Channel in small boats in 2022. Gareth Fuller
The concerns within the Government come after Rishi Sunak vowed to curb Channel crossings in December, declaring "enough is enough".
The Prime Minister said it was "unfair people come here illegally" as he outlined his plan to reduce the numbers washing up on UK shores in small boats.
His blueprint included a new pact with Albania to return migrants with no right to be in Britain.
In 2022 almost 13,000 of those who crossed the English Channel came from the Eastern European country.
However, ministers worry Mr Sunak has oversold his migration plan, with the number of crossings to remain high in the months to come.
A senior government source told The Times: "Even if you stopped any more Albanians coming across, the boats would still travel.
"Their places on the boats would be filled by Somalis, Eritreans or Afghans who can’t afford to pay as much as the Albanians.
"There is an almost infinite number of people who want to come to the UK."
In 2022, a record 45,756 people were recorded as having arrived in Britain via small boats. The figure is 60 percent higher than in 2021, with the numbers rising year-on-year since 2018.
Rishi Sunak vowed to curb illegal crossings last month as he declared 'enough is enough' UK Parliament/Jessica Taylor
Last year also saw the highest number of crossings every recorded in a single day, with 1,295 people making the treacherous journey across the English Channel on August 22.
A Home Office source added: "No one is saying illegal migrants from Albania is the only issue we face.
"That’s why the prime minister and the home secretary have a plan to tackle illegal migration across the Channel in small boats, irrespective of the nationality of those making the journey, and they will be bringing forward new legislation to target this as soon as possible."
As well as the deal with Albania, Mr Sunak's plan unveiled last months included UK Border Force personnel patrolling beaches with French officers and new legislation to stop "late or spurious" legal appeals.
No10 says it also remains committed to the Rwanda deportation scheme.