The firm has confirmed it is closing 89 branches as part of a planned consolidation of its retail estate and offering options for alternative work to staff.
Hays took over 555 Thomas Cook stores when the firm collapsed in 2019 and had put off reviewing their performance during the coronavirus pandemic to see if business picked up this year.
But the firm says the third national lockdown and travel ban meant it had to act.
Chief Operating Officer Jonathon Woodall said the company would begin consulting with 388 retail staff on potential options to reduce the number of redundancies: “Our first priority is to continue to look after our customers and we offer the highest standards of customer service through our retail, phone and online divisions,” he said.
"We are continuing with our robust two-year business plan and continue to be ready for the bounce back when it comes.”
Dame Irene Hays, owner and chair of Hays Travel, said: “It was always our intention to review the performance of our shops at the end of the licence period - we had hoped the business would bounce back in January and it has not.
"We have done everything we could to safeguard jobs and the business thus far, and we have come up with a range of options for those at risk of redundancy to help as many colleagues as we can.”
Among other options, staff will be offered the chance to join the Hays Travel Homeworking Division, to work from home, or take positions in other shops where there is a vacancy.
Travel industry trade union TSSA said it was a ‘a sad but inevitable move’ and accused the government of recklessness.
General Secretary Manuel Cortes said: “With coronavirus rampant and the usual January booking of summer holidays absent, the travel trade continues to suffer.
“The Coronavirus has fundamentally changed our way of life and our ability to travel, but the government has been reckless in its failure to act.
"We should have had border restrictions and effective test, track and trace implemented last spring when the virus levels could have been controlled.”