The Home Office is more than 1,400 short of its target staffing level for Brexit preparations.
MPs heard the department assesses that its activities related to departure from the EU require a total of 4,100 personnel across Border Force, UK Visas and Immigration, Immigration Enforcement and other functions.
With less than five months to go before the UK leaves the EU, there are currently 2,662 staff in post.
Officials said the remaining 1,438 are "in the pipeline" or will be drawn from ongoing recruitment campaigns.
But Labour MP Yvette Cooper, who chairs the Commons Home Affairs committee, described the shortfall as a "pretty stonking great gap".
'Information is the lifeblood of border security'
It was also disclosed that the Home Office is stepping up its preparations for a no-deal Brexit.
Sir Philip Rutnam, permanent secretary at the department, said if it was clear that the outcome was no-deal, there would be "enormously intensive activity" from Christmas onwards.
Under the plans, immigration enforcement personnel could be switched to strengthen the border, but deployment of the military was not being considered.
Sir Philip told the Committee: "It is not part of our no-deal planning that we would deploy the armed forces, for example at the border."
He confirmed that in a no-deal scenario, it is anticipated that there would be a reduction in information available at the border.
Sir Philip said: "Information is the lifeblood of border security and law enforcement. It's a vital resource so any reduction is to be deeply regretted.
"There would be an effect. However, to reassure you and to reassure the public, we, in the context of our no-deal planning, are doing everything we can to try to mitigate this effect."