Professor John Edmunds, a member of Sage and the sub-group SPI-M, said the numbers are likely to decline “some time in the autumn” but warned they could rise again in the spring.
His comments came as the government came under increasing from some health experts to introduce plan B measures, which would see compulsory face masks, home working and vaccine passports.
Labour has backed calls for tighter measures but Rishi Sunak, the chancellor, ruled out bringing in plan B.
In broadcast interviews on Sunday, he said there was nothing in the data to suggest extra restrictions are required but added that ministers are “keeping an eye” on the data.
Some 39,962 new cases were recorded on Sunday, down from 44,985 on Saturday, although the figures are typically lower on a Sunday.
Speaking to the Daily Telegraph Professor Edmunds, of the London School of Hygiene and Tropical Medicine, said modelling carried out by the university showed cases are likely to decline in the coming weeks.
He said: “When we were doing the work about two weeks ago, the Health Secretary had made it very clear that the government was not planning to introduce Plan B in the near future.
“Our model was projecting that cases would start to decline some time in the autumn.
“However, the model also suggests that cases may start to climb again in the spring, due to a combination of waning immunity and increased contacts.”
But Peter Openshaw, a member of the New and Emerging Respiratory Virus Threats Advisory Group, said case numbers and death rates are currently “unacceptable”.
He encouraged members of the public to take “matters into your own hands” and suggested people should not wait for government policy before changing their behaviour to help stop the spread of the virus.
On Monday morning Sajid Javid, the health secretary, said he believes “we’ll have a normal Christmas” this year as he urged people to come forward and get their vaccines and booster shots.
He told BBC Breakfast it is not necessary to implement plan B of the winter Covid-19 precautions “at this point”.
Asked about the festive season, he said: “This virus, we’ve seen already, what we know about it is it is unpredictable and I don’t think any sensible health secretary across the world would want to predict exactly where we’re going to be in three months’ time, or six months’ time, not least because there’s always the risk sadly of a new variant that could be more dangerous.”
But he said the best thing to do is get vaccinated and take daily precautions.
He added: “For all those people like me that are hoping and planning for a normal Christmas – which I do by the way, I think that’s where we’ll be, we’ll have a normal Christmas – if we want let’s just keep playing our part.”