Migrants are being moved out of an overcrowded immigration centre.
The union representing Border Force staff working at the Manston site in Kent said the Home Office hoped to take 400 people out of the site on Tuesday.
Lucy Moreton, of the Union for Borders, Immigration and Customs (ISU), also said the Government department had not responded to its requests for increased support for staff working at the processing centre near Ramsgate.
Two coaches with heavily tinted windows were seen leaving the centre at around 4.15pm on Tuesday. It appeared the buses were full of people.
Another coach entered the site at around 4.25pm.
A Home Office spokesman said the department would not provide a “running commentary” on the number of people currently at the site.
On Tuesday evening, immigration minister Robert Jenrick said the number of migrants at Manston has “fallen substantially”.
He said: “Unless we receive an unexpectedly high number of migrants in small boats in the coming days, numbers will fall significantly this week.
“It’s imperative that the site returns a sustainable operating model and we are doing everything we can to ensure that happens swiftly.”
Sir Roger Gale, the Conservative MP for the North Thanet constituency which includes Manston, later said on Twitter that “several hundred” had already been relocated.
It is unclear whether those moved from Manston will be taken to hotels or alternative accommodation.
The site, located at a former Ministry of Defence fire training centre, opened in January 2022 and was designed to hold up to 1,600 people for no more than 24 hours.
But on Monday Sir Roger said there were currently 4,000 people being held at the site and the situation there was a “breach of humane conditions”.
Speaking to the PA news agency, Ms Moreton said: “I don’t know yet how many will go today but yesterday we were told the aim was to move 400.
“Sadly, nothing is being done to relieve the pressure on staff.
“We have asked the Home Office for increased support, for wellbeing and mental health services and for assurances to address staff concerns around the legality of instructions they are being given, the sustainability for the short and medium term and any ongoing threat to staff.
“The Home Office have not replied.”
The department said it takes the welfare of staff extremely seriously, recognises the work they are doing to ease the situation and is committed to the safety of both staff and the migrants.
Meanwhile the British Red Cross said “immediate action” needs to be taken to remedy the situation at Manston.
Alex Fraser, director of refugee services and restoring family links at the charity, said: “We are extremely concerned about the escalating humanitarian situation at Manston.
“It’s clear that immediate action is required to ensure that the men, women and children who have just made a dangerous and potentially traumatic journey have their basic needs met in a safe environment.
“No one should experience overcrowded accommodation that puts them at risk of disease and potentially being detained unlawfully. We know from our work supporting people in similar temporary accommodation what a damaging impact it can have on them.
“Sadly, the serious problems at Manston are indicative of the wider issues facing the asylum system.
“The UK Government needs to urgently look at ways of reducing the backlog of asylum decisions, including making quicker decisions for nationalities who typically have their asylum claims approved, and providing more safe routes so people who have been forced to leave their homes do not have to make dangerous journeys and gamble with their lives.
“Our country has a proud history of helping people fleeing war and persecution. It doesn’t matter how you got here, everyone deserves to be treated with compassion and humanity once you’re on our shores.”