Upper Crust owner SSP Group says up to 5,000 jobs could be cut across its UK outlets and head office, as it struggles with the reduction in passenger travel.
The firm said global sales in April and May were 95% below the previous year's.
SSP operates 580 food and drink outlets across the UK, mostly at railway stations and airports, but fewer than 10 are currently open.
The company expects only one-fifth of its UK stores to be open by the autumn.
SSP employs around 39,000 staff worldwide across 2,800 outlets. Last month, it said it had suffered "extremely low sales" after the coronavirus pandemic forced it to shut branches.
As well as Upper Crust bakeries, the company also owns the Caffè Ritazza chain, deli operator Camden Food Co. and luxury bar chain Cabin.
SSP joins a growing list of companies slashing jobs as the UK economy suffers its worst contraction in 41 years.
In the past few days, a number of firms have announced UK job cuts:
- Aerospace giant Airbus has said it wants to cut 1,700 jobs in the UK, as part of plans to shed 15,000 posts across the whole company
- Cutbacks at EasyJet mean nearly 1,300 UK crew members and 727 pilots are at risk of losing their jobs at the airline, unions say
- About 600 workers at shirtmaker TM Lewin will lose their jobs as the firm's 66 stores are closed
- Royal Mail has said it is to cut 2,000 management jobs
"Covid-19 continues to have an unprecedented impact on the travel industry and on SSP's businesses in all geographies," said SSP Group chief executive Simon Smith.
"We are beginning to see early signs of recovery in some parts of the world and are starting to open units as passenger demand picks up. However, in the UK the pace of the recovery continues to be slow," he said.
The company added: "If the pace of the recovery continues at the current level, this could lead to up to c. 5,000 roles becoming redundant from within the head office and UK operations."
While SSP operates across more than 30 countries, including the US, India and China, the job cuts are only being made at its UK business.
At this time of year, the company would normally employ about 9,000 people across the UK. Staff have been enrolled on the government-paid furlough scheme throughout the coronavirus crisis.
The company said it had planned to reopen UK outlets as passenger demand returned, adding: "The reality is that passenger numbers still remain at very low levels."
Mr Smith said the firm would swiftly reopen UK units if there were improved sales over the summer.
In a statement, the company said it had access to around £750m in liquidity and it was confident it had sufficient funds to allow it to operate "throughout even its most pessimistic scenario".