Bevan - who worked for a number of restaurant groups including Nobu and Ping Pong prior to taking on the first floor restaurant - doesn't believe that tourists will return in significant numbers until next year but is hopeful that some office workers will come back to the area after the summer holidays.
Speaking on the latest Restaurant podcast, Roast Restaurant's owner says he will probably re-open in late September.
"I'm like a caged animal. Nobody is keener to get back into the business than me. But Roast is a large restaurant - we have 140 covers to fill and we need to take £170,000 a month to break even.
"We don't feel we can achieve that currently. We've had cameras installed looking down into the market so we can see how busy it is day or night. It's not good in Borough Market at the moment, I would say the footfall down at least 80%. We need to retain cash to move forwards and we don't want to make any losses."
The first floor location has always been a challenge and the situation has been further complicated by landlord Borough Market's promotion of alfresco dining for the summer months.
Prior to the pandemic, Roast Restaurant traded right through the day - it's always been a popular choice for breakfast and more recently afternoon tea - but this is likely to change for the short to medium term.
"We might not open Monday and Tuesdays. We need to maximise our chances of success going forward. We're going to have to watch every pound and every hour."
A number of staff have already been made redundant.
"We had 80 staff at roast. We just couldn't have maintained that. It's a dreadful scenario. We've tended to keep people that have flexible skills, for example those that can work both the floor and the bar. That way we can move people around."
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