It had warned that only around a fifth of its sites in the UK would open by the autumn, but it has been able to reopen more sites as sales have improved slightly since full lockdown restrictions eased.
The latest restrictions brought in on Tuesday by the Prime Minister, including instructions for office staff to work from home where they can, are likely to deal another blow.
SSP cautioned that demand “may well remain subdued” over the winter months.
Simon Smith, chief executive of SSP Group, said: “We have seen some improvement in passenger demand since the start of the crisis and we have reopened units swiftly and profitably in response to this, with over one-third of our units now trading.
“Our model is flexible and we will continue to align unit openings with demand, meeting the needs of our customers whilst managing operating costs and cash flow tightly.
“In the medium term we expect to see the gradual return of passenger travel to more normalised levels.
“The actions we are taking to rebuild the business will enable us to emerge fitter and stronger.”