MPs claimed it is already stretched due to “inadequate resources”, raising concerns over the impact of a major increase in activity for the agency.
Ministers were urged to set out whether they want additional border checks on Europeans after Britain’s departure in March 2019.
In a report published on Wednesday, the Commons Home Affairs Committee said: “It is clear to us that Border Force does not currently have the capacity to deliver this and will struggle to put sufficient additional capacity and systems in place.”
The paper urges the Government to be “realistic” about the lack of time left to make substantial changes to border arrangements before March next year, adding: “Rushed and under-resourced changes will put border security at risk.”
Citing a warning from inspectors about “poor” coverage of minor harbours and landing places along the east coast, the report adds: “We are increasingly alarmed about the impact that inadequate resources are having on the capacity for Border Force to operate effectively.”
Last year the Home Office launched a recruitment drive to add 300 extra personnel to Border Force, which is responsible for carrying out immigration and customs controls on people and goods entering the country.
Figures show the body had 7,670 full-time staff on average in 2016-17 – down by 241 compared with the previous year.
As well as the findings on Border Force, the committee’s assessment concludes that delays to a proposed white paper on immigration have caused anxiety for EU citizens and uncertainty for businesses.
It also says it would not be feasible to establish two “smoothly functioning” registration schemes – one for existing residents and one for new arrivals after Brexit day.
Labour MP Yvette Cooper, who chairs the committee, said: “The Government does not seem to appreciate the immense bureaucratic challenge they are facing or how much time and resources they need to plan on Brexit.
“The Home Office will end up in a real mess next year if there isn’t enough time to sort things out.”
A Home Office spokeswoman said: “It is ridiculous to suggest that we are not preparing sufficiently for leaving the EU.
“It is precisely for this reason that we have already invested £60 million in 2017/18, are planning to recruit an additional 1,500 staff across the immigration, borders and citizenship system and are well advanced in the development of a new scheme to give EU citizens currently here the right to stay after Brexit.
“We will keep staffing under review as negotiations progress, but will always ensure we have the resources and workforce we need to run an effective system.”