In response to a Freedom of Information request by the Telegraph, officials at the Home Office revealed at least 1,000 people are set to be removed from the country and sent to France, Italy and Germany.
A record 416 migrants arrived in the UK on small boats earlier this month, the most ever on a single day.
The total number of migrants who have crossed the sea to Britain in 2020 is now more than 5,600, analysis shows.
Officials at the Immigration Enforcement Secretariat told the Telegraph the Channel crossings were “thoroughly unacceptable” and said that the Government and Ms Patel are “equally frustrated by the severity of the situation”.
“There is considerable policy work underway to address where the UK’s immigration and asylum system is being exploited and abused," said the response.
"As it currently stands, the system is inflexible and rigid, and is open to abuse by both migrants and activist lawyers to frustrate the returns of those who have no right to be here.”
The comments come after the Home Office was forced to abandon using a video which accused “activist lawyers” representing migrants of trying to disrupt the asylum system after a barrage of complaints.
Amanda Pinto QC, chair of the Bar Council, said that lawyers should not be political targets for simply doing their jobs.
She added: “Irresponsible, misleading communications from the Government, around the job that lawyers do in the public interest, are extremely damaging to our society.
“Legal professionals who apply the law and follow Parliament’s express intention, are not ‘activists’.
The unnamed civil servant who responded to the FOI request said the Home Office is urging the French Government to “take more urgent and productive action to patrol the French coastline”.
“We have offered to bolster surveillance, policing and patrols in collaboration with French police patrols on their beaches and this is subject to further discussions with them," they wrote.
One flight left the UK on Tuesday but a second flight to Spain was prevented from taking off following a last minute intervention by lawyers.
It comes after a scathing review from the Public Accounts Committee accused the Home Office of of basing immigration policies on “anecdote, assumption and prejudice” instead of evidence, and having no idea of the effect they have on migrants.
The findings published on Friday, said the Home Office has “no idea” what its £400 million immigration enforcement annual spending achieves, and instead appears to formulate policies not on evidence but on “anecdote, assumption and prejudice”.
Committee chairman Meg Hillier said: “The Home Office has frighteningly little grasp of the impact of its activities in managing immigration.
“It shows no inclination to learn from its numerous mistakes across a swathe of immigration activities – even when it fully accepts that it has made serious errors.
“It accepts the wreckage that its ignorance and the culture it has fostered caused in the Windrush scandal – but the evidence we saw shows too little intent to change, and inspires no confidence that the next such scandal isn’t right around the corner.”
Despite “years of public and political debate and concern”, the department still does not know the size of the illegal population in the UK, the report said.
A Home Office source said: “The Home Secretary agrees with the assessment made by the Public Accounts Committee of historical issues at the Home Office.
“She has spoken at great length how the department puts process before people and is why she has committed to implementing the findings of the Wendy Williams review into Windrush.”
The Evening Standard has contacted the Home Office for further comment.