Fifteen are in the process of being removed from the UK while 14 were placed on immigration bail pending further investigations.
Site sources said the swoop last Thursday morning was a major operation by the Home Office as Albanian, Indian and Lithuanian nationals were detained.
One told the Enquirer: “It took everyone by surprise and they got a lot of people but quite a few more jumped over the site fences when they realised what was happening and were away.”
The Enquirer understands that seven of those detained were working for concrete frame specialist Getjar.
A BAM spokesperson said: “Home Office officials visited King’s Cross on Thursday 11th July and detained 29 operatives for further questioning.
“Those detained were part of the supply chain.
“We are committed to ensuring those working on our sites are legally eligible to do so, and will continue to work closely with our subcontractors to ensure thorough checks are being carried out.
“Construction activity at King’s Cross remained unaffected.”
BAM refused to confirm exactly which of its sites was raided.
The contractor is working on a number of sites for developer Argent at King’s Cross including a £200m job to build a new headquarters for Facebook.
Argent also declined to comment.
A spokesperson for Getjar said: “Home Office officials visited King’s Cross on Thursday 11th July and detained individuals working on site for further questioning.
“The majority of these individuals have subsequently been released and allowed back to work. GetJar is committed to fully complying with UK labour laws and we frequently review our internal policies to ensure they meet best practice.”
The Home Office said it had been “acting on intelligence” to stage the raid.
A spokesperson said: “28 people of Albanian and Indian nationalities, plus a Lithuanian national who was subject to an outstanding deportation order, were arrested for immigration offences.
“15 were detained pending removal from the UK, while the remaining 14 were placed on immigration bail while their cases are progressed.”