The coronavirus R number in the UK has remained largely unchanged since last week and is now estimated to be between 1.2 and 1.3.
Figures released by the Government Office for Science and the Scientific Advisory Group for Emergencies (Sage) also put R between 1.1 and 1.3 in England.
Last week R was between 1 and 1.4 in the UK, and between 1.1 and 1.4 in England.
The R rate refers to the number of people that an infected person will pass the virus on to, with an R rate above 1 meaning the epidemic is still growing.
But experts advising the Government have said that areas that have been under tougher restrictions for a longer period of time – including east of England, London, and the south east – are showing “a slight decline in the number of people infected”.
But they warned that regions such as the north west and south west continue to see infections rise, where the spread of the new UK variant may be playing a role.
The Sage scientists said that the estimates are based on the latest data, available up to January 11.
They added: “The latest figures show that we need to remain vigilant to keep this virus under control, to protect the NHS and save lives.
“We all need to play our part and if everyone continues to follow the rules – we can expect to drive down the R number across the country.”
Meanwhile, Cambridge University researchers have said the R is below 1 in the east of England, London, the south east, West Midlands and Yorkshire and the Humber.
But they believe it is still above 1 in the south west, north west, north east and the East Midlands, indicating case numbers are growing in those regions.
It comes as Public Health England (PHE) released data on Wednesday showing that infection rates had fallen in most regions of England across all age groups apart from the over 80s.
At the same time, however, the PHE surveillance report noted that there were more people being admitted to hospitals and intensive care units.
NHS England data shows that around one in five major hospital trusts in England had no spare adult critical care beds on January 10.
Elsewhere, the Zoe Covid Symptom Study UK Infection Survey from King’s College London put the UK R rate at 0.9.
It showed that cases have also plateaued in most age groups.
Professor Tim Spector, who is leading the study, said: “It’s great to see case numbers falling in most regions but numbers are still worryingly high and hospitals will stay under pressure for some time yet.
“With such high numbers and growing evidence new strains are highly transmissible, things can still take a turn for the worse. We need numbers to keep falling before we make any changes to current restrictions.”