British MPs have been told there is a serious risk of fire, unrest and infection breaking out at the Manston facility in Kent.
Opened in January, it was designed to hold migrants for no more than 24 hours.
However, a British immigration official who visited the site said he met several families who had been detained there for weeks.
Giving evidence to the home affairs select committee in Parliament, David Neal, independent chief inspector of borders and immigration, said he was shocked to learn that some security staff guarding detainees are unqualified.
“It was sufficiently alarming when I discovered that, I was frankly speechless and I’m not someone who is normally speechless,” he told the committee.
Mr Neal described what he saw during his visit as “pretty wretched conditions” and said it was “a really dangerous situation”.
“I spoke to an Afghan family who had been in a marquee for 32 days,” he said. They were most likely sleeping on kit mats on the floor, he said.
“I spoke to an Iraqi family … who had been in buildings and they had been there for two weeks. And a Syrian family who had been there for two weeks as well. The mother is terribly distressed because she didn’t know where they were going.”
Following his visit to the site on Monday, he said he wrote a letter to the then-home secretary Grant Shapps, to alert them to the situation.
After being sworn in as prime minister on Tuesday, Rishi Sunak appointed Suella Braverman as home secretary, a move which has caused controversy.
A week earlier then-prime minister Liz Truss sacked Ms Braverman for breaching the ministerial code when she sent a secure document to a person outside the government via her personal email.
A full-time doctor began working at Manston on Monday and proposed that a five-bed ward be built to treat patients.
In the past two months there have been four cases of diphtheria found in the 11,000 people who passed through the facility, he said. The infection can cause difficulty breathing, heart rhythm problems and death.
Labour MP Dame Diana Johnson, chairwoman of the committee, posed an urgent question in the House of Commons on Thursday, asking the home secretary to speak on the situation in Manston. Ms Braverman failed to turn up, instead sending immigration minister Robert Jenrick to give details.
Dame Diana said she was “very disappointed” that Ms Braverman did not attend to answer the question, and said the situation at Manston “constitutes a major incident that is escalating in severity”. She said the number of people detained at the site makes Manston “larger than any prison in this country” and “vastly outstrips” its capacity to cater for 1,600 individuals.
“There is a serious question about the legality of detaining people at the facility for more than 24 hours,” she said.
Mr Jenrick said the continuous rise of illegal Channel crossing was “placing an unprecedented strain” on the UK’s asylum system.
There are 2,636 people at Manston waiting to be moved to hotels, he said.
He said the government wanted to ensure site was “maintained legally”. The government was committed to building a fair immigration system that allows people to come to the country legally, while being “robust” for those choosing to make the journey illegally, he said.
He said many migrants who arrive in the UK via illegal routes came from safe countries, including France.
The home affairs select committee was on Wednesday told that about 10,000 men from Albania had travelled to the UK in small boats since the start of the year.
The figure, from the Home Office, represents up to 2 per cent of all men aged between 20 and 40 in the southern European country.
Dan O’Mahoney, clandestine Channel threat commander for Border Force, said the “exponential rise” was because of Albanian criminal gangs operating in northern France.