"The government is a customer of Carillion, and our focus has been on ensuring that we are providing the public services - they are continuing to be provided uninterrupted - to reassure workers on those public services that they will get paid, to reassure the pensioners and ensure support is there for them", May said at Prime Minister's Questions on Wednesday.
"What we said to Greg Clark yesterday was we need more time, those companies need more time and we've suggested this taskforce be set up that is led by the government, that includes trade unions representing the workers, that includes businesses".
"Time is of the essence in dealing with this crisis". There are fears about jobs, pay and pensions, all of which will need addressed.
The Trades Union Congress (TUC) is part of the task force and is pressing for the transfer of private sector contracts to alternative providers with jobs, pay and pensions protected.
Earlier, building society Nationwide said it was safeguarding the jobs of 250 Carillion workers employed on services such as cleaning and security by taking their roles in-house.
'There is an exercise going on to make sure that all the contractors are identified, that they are given assistance from the banks, which is very important, but also - because most of these contracts are profitable - that they can be reassigned and can continue, ' said Mr Clark.More news: Winter Storm Jaxon targets Denver and midwest
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The TUC is also calling for protection for agency and zero-hours workers at Carillion projects, and a risk assessment of other large outsourcing firms.
Its failure means the government will have to provide funding to maintain the public services run by Carillion.
Lenders are now contacting customers, the government said, and are putting in place emergency measures where needed, including overdraft extensions, payment holidays and fee waivers to ensure those facing short term issues can be helped to stay on track.
Lloyds Banking Group meanwhile said it would launch a 50 million pound fund to help small businesses within Carillion's supply chain that may be experiencing financial difficulty.
Mr Cherry said that Carillion's collapse had highlighted the problem of late payments, which should be stopped "as a matter of urgency".
Construction industry body Build UK has estimated there are 25,000-30,000 businesses owed money for work carried out for Carillion prior to the allegation.