Imperial College London Professor of mathematical biology Neil Ferguson made the statement on Monday (local time).
"We think the epidemic is just about slowing in the UK right now," Ferguson told BBC radio.
Patrick Vallance, the government's chief scientific adviser, also said there were signs that locking down the country a week ago had slowed the rate of transmission of the virus. He said Britain was not in a "fast acceleration" phase.
Official data showed 1408 patients in the UK who tested positive for coronavirus (COVID-19) had died and there were 22,141 positive cases.
Britain initially took a modest approach to containing the spread of the disease compared with European countries such as Italy.
But Prime Minister Boris Johnson imposed stringent controls after projections showed a quarter of a million people could die. Johnson has since become the first leader of a major power to announce a positive test result for coronavirus.
Vallance said the restrictions - which have seen public transport use fall to less than a quarter of normal levels - were already having a "big effect" on the transmission of the virus.
This in turn would to lead to fewer people being admitted to hospital, he said, and ultimately reduce the total fatality figure.
Hospital admissions had already stabilised at about 1000 per day, he said.
"It's quite important - it tells you that actually this is a bit more stable than it has been," he said, adding that the country was tracking France rather than the worse-hit Italy and Spain.
He said it would take another two to three weeks to determine the extent of the slowdown in the spread of the virus because of the lag between the rate of transmission and that of hospital admissions.
Ferguson said a third or even 40% of people do not get any symptoms and thought perhaps 2% to 3% of Britain's population had been infected.
But Ferguson cautioned that the data was not good enough to make firm extrapolations.
He said antibody tests were in the final stage of validation and could hopefully be ready in "days rather than weeks".
