Defence chiefs are increasingly unhappy with their role in controlling small boats in the Channel, according to the Observer.
Ministry of Defence data shows that crossings have almost doubled since the military were given authority over the situation in mid-April.
The government was warned that using the Royal Navy would increase the crossings, but they ignored the advice.
A former defence minister told the newspaper that the navy was now in effect providing an “efficient taxi service” for refugees.
Naval commanders have told the defence committee that using the navy is not a deterrent, but makes the crossing safer and more appealing for small boats.
Enver Solomon, chief executive of the Refugee Council, said that using the navy “demonstrates how the government is obsessed with control over both compassion and competence.”
He added: “Using the military to repel [refugees] and seeking to expel them to Rwanda is a nasty and brutish response.”