Burger King, which has outlets at Clifton moor as well as York station, has said it hopes to open at least 350 of its restaurants by the end of June as part of a staggered re-opening after the lockdown.
It has already announced plans to open 12 restaurants out of its current crop of 500.
Speaking to the BBC’s World At One programme, UK chief executive Alasdair Murdoch said: “We would anticipate that by the end of June, we will be getting towards 350 and 400.
“We see that some of the others will be difficult to open – some are in airports.
“At this stage none of us really have the visibility on when they might do.”
He said a scaled-back menu would allow staff to socially distance while making the food, with the arrangements being put into place for drive-through restaurants and with trials set to start on how to re-open high street walk-in locations.
Mr Murdoch said Burger King would face “difficult decisions” on staffing if it did not re-open its restaurants.
“I don’t necessarily think we will have to sack staff,” he told the BBC when asked if some furloughed staff would have to be let go when the Government’s offer ends.
“The challenge for us lies around the support that might be there or might not be there in that point in time.
“I think it is too early to say that. We will try to do everything we can to avoid doing that.
“But the more we open, the fewer people we will have to face those difficult decisions with in the long-term.”
The company has called for action on rents, asking for a “national time-out scheme” whereby the Government would provide landlords and tenants with a nine-month rent holiday.