Parcel delivery company City Link, which employs 2,727 people, has gone into administration.
The Coventry-based company, owned by investment firm Better Capital, called in administrators on Christmas Eve after "substantial losses".
RMT union general secretary Mick Cash told the BBC: "The way it's happened... that on Christmas Day they've done this to our members is disgraceful."
Administrators warned of "substantial redundancies" over the coming days.
This is because no buyer has been found to save the company.
A number of staff will be retained to help return parcels to customers and help with winding down the company, said administrators Ernst & Young.
City Link has stopped accepting parcels from customers at its head office and transport hub in Coventry, its three other transport hubs and 53 UK depots.
Operations will be suspended at all the company's depots until Monday when customers and recipients will be able to collect their parcels, which they have been urged to do as soon as possible.
The firm's online parcel tracking system remains live and a help phone will be open on Saturday and then from December 29.
Hunter Kelly, of Ernst and Young, said: "City Link Limited has incurred substantial losses over several years.
"These losses reflect a combination of intense competition in the sector, changing customer and parcel recipient preferences, and difficulties for the company in reducing its cost base.
"The strain of these losses became too great and all but used up Better Capital's £40m investment, which was made in 2013 and intended to help to turn around the company.
"Despite the best efforts to save City Link Limited, including marketing the company for sale, it could not continue to operate as a going concern and administrators were appointed.
"We will provide support to employees relating to potential redundancies. We are now beginning the process of realising the company's assets."
'How will I eat?'
One City Link worker, who wished to remain anonymous, called the situation "utterly disgraceful".
"I worked on Christmas Eve with no warning this would happen; I found out from the news," he said.
"I am so furious with what has happened, I have no idea what I'll do. I have no money since it's Christmas so I don't know where next month's rent will be coming from, where will I live? How will I eat?"
Simon Judd, from Leigh-on-Sea in Essex, said: "I'm a sub-contractor with City Link, now find I have a liveried van and no work."
He added: "They've got rid of most employed drivers at my depot, and presumably nationwide. Just have to hope I can find some work elsewhere, after getting van made white."
Mr Cash said: "We're in a situation where at one stage in the last few weeks we've had a lot of media coverage going around saying people can't have delivery of parcels because there is not enough capacity - yet a going concern like this goes into administration.
"This is the bitterest blow any group of workers could receive on Christmas Day and it is absolutely shocking that the company have sprung this announcement once all the Christmas deliveries have been completed.
"RMT will do everything within its power to mobilise a political and industrial fight to save the thousands of jobs that have been put at risk as a result of this shock announcement."
The RMT told its members on Christmas Eve that it understood that wages owed up to 31 December would be paid, but any further payments are not guaranteed.
Founded in 1969, City Link said on its website it had annual revenues of approximately £300m, a fleet of 1,700 vehicles and delivered 60 million items across the UK and worldwide each year.