Passengers arriving into Gatwick last night (April 30) were left with delays of up to four hours following an IT glitch.
The problem, which affected Border Force computer system, also impacted on several other UK airports including Heathrow.
The Government has today apologised but declined to specify how many airports are still affected by the problem.
Travellers arriving into the UK last night were told to expect slow-moving queues lasting for up to four hours as staff battled to resolve the issue.
Immigration and security minister James Brokenshire said this morning: "Our engineers have been working through the night to fix the temporary IT problems that regrettably led to longer queues for some passengers at passport controls yesterday.
"The current situation is much improved and we are doing our best to keep waiting times to a minimum during this morning's busy period.
"We apologise for any delays but security must remain our priority at all times."
A Home Office spokesman refused to provide "a running commentary" on the situation.
But they said Mr Brokenshire had been kept updated on the situation through the night and would be at Heathrow this morning with the director general of Border Force to personally oversee the ongoing work to resolve the situation.
Gatwick Airport said an IT glitch affecting the Border Force computer system has been resolved.
The technical problem affected immigration desks at airports and ports nationwide, resulting in lengthy queues for passengers.
Gatwick Airport tweeted: "Yesterday's difficulties with (UK Home Office) IT systems have now been resolved."
Chris Hyland, a 32-year-old company director from Islington in north London, said international passengers at Gatwick had been told to expect a wait of up to four hours last night.
He said: "We landed from Geneva at 5.20pm but it took until 6.40pm for us to get through passport control.
"It's an absolute nightmare. We've been told there is an IT failure but that's it.
"You would have thought there would be a back-up plan."
Mr Hyland said non-EU passengers are preparing for a long wait to officially enter the country.
He said: "It is very frustrating. Nobody is really saying anything.
"The international queue is pretty huge, so people have already started sitting down because they know they will be there for a long, long time."