Metro mayors in the North West of England have made an "urgent" call for the release of regional Covid-19 reproduction rate figures.
Andy Burnham and Steve Rotheram said their regions had "the highest number of new cases last week".
In a letter to the prime minister, they said relaxing the Stay at Home message "may have come too early" for Greater Manchester and Liverpool City Region.
The government took the right steps at the right time, a spokesman said.
The reproduction, or R number, is a way of measuring the ability of a disease to spread. It is the average number of people that one infected person will pass the virus on to.
Mr Burnham and Mr Rotheram wrote to Boris Johnson on Tuesday to request publication "as a matter of urgency" of an "up-to-date reproduction 'R' number at a regional and sub-regional level on a daily or regular basis".
"We believe this is essential information which will help our residents make informed decisions about the risk and help decide whether they wish to take a more cautious approach to the relaxation of the lockdown rules, given the risk locally", they wrote.
They said the move would also "reduce the risks of regional or local lockdowns".
The mayors pointed out that their regions are "not yet on the clear downward trajectory seen in other parts of the country".
The Health Service Journal has reported the spread of the virus appears to be persisting at a higher rate in parts of the north of England, which has prompted "warnings that the mortality gap between those more and less deprived will get bigger".
It quoted a warning from a group of scientists, led by former chief scientific adviser Sir David King, who said "the changes to the guidance are 'dangerous' and that 'further local COVID-19 epidemics are inevitable'".
The mayors expressed "disappointment over the lack of meaningful consultation and advance knowledge of the changes" and concern about "the substance of what was announced".
'Avoid a second spike'
North of Tyne Mayor Jamie Driscoll supported the call, saying it "would help us work with our businesses and public services to keep people safe."
"Clearly the government wants to ease restrictions as soon as they can. If they want people to 'stay alert' that means sharing information.
"That also means giving us the levers to do something about it. Economic recovery and public safety are inseparable. We have to avoid a second spike in infections."
Mayors across England's biggest urban areas earlier warned that new lockdown rules, which came into force on Wednesday, are confusing.
A government spokesman said: "We have taken the right steps at the right time based on the best available science to tackle coronavirus and keep the whole of the UK safe.
"The sacrifice of people across the country by following social distancing rules means we can begin to gradually reopen our society.
"But as the Prime Minister said, this will only happen if everyone stays alert, continues to follow the rules, and the rate of infection stays down."