Leicester's mayor has called for 90% of the city's lockdown to be lifted and said residents will be "very angry" if restrictions are extended further.
A prolonged lockdown for the city was announced on 29 June after a spike in Covid-19 cases, with non-essential shops and schools closed.
But mayor Sir Peter Soulsby said new data showed only 10% of Leicester had seen higher transmission rates.
The health secretary is due to rule on whether to extend restrictions later.
The Department of Health and Social Care previously said it "makes no apology" for trying to reverse infection rates.
Sir Peter said the government had got local people into a "messy situation" by its handling of the restrictions.
On the prospect of the local lockdown being extended, he said: "I think if we are told that, there are going to be an awful lot of Leicester people who are very angry indeed."
Sir Peter criticised the access to data city authorities had been given, saying: "I very much regret the fact that the government didn't trust us with this data earlier.
"But I think now we've got it, we are the ones well-placed here in the city to make sure that we use it effectively."
He added: "I hope that [the health secretary] will allow us and trust us at a local level to work with the people of the city - and to recognise that the other 90% of the city that has been locked down, along with the area that is of concern, should be allowed to go free with the rest of the country."
Health Secretary Matt Hancock said information covering the period since local measures were introduced would be looked at, followed by a public announcement "as soon as is reasonably possible".
On a visit to Nottinghamshire, Labour leader Sir Keir Starmer said lessons should be learned from Leicester's experience.
He said: "Act more quickly - the government delayed 11 days between first announcing that there was a problem in Leicester and actually going into lockdown.
"The second thing is - share the data. People on the ground... weren't getting the data shared with them in a timely manner."
Speaking in the House of Commons, Leicester West MP Liz Kendall criticised the government's handling of the situation, saying decisions were not shared promptly, leaving businesses and residents confused.
In response, Health Minister Nadine Dorries said they had been in close consultation with local officials and it was the mayor, along with Leicestershire County Council leader Nick Rushton, who had drawn the lines on the lockdown map.
On Wednesday evening, Mr Hancock said the government would base its decision on whether or not to extend the local lockdown on "14 days of data".
The most recent data from Public Health England shows the number of new cases of coronavirus per 100,000 population in Leicester has dropped from 127.2 in the seven days to 5 July to 104.4 in the seven days to 12 July.
It was 143.6 in the seven days to 28 June, just before the local lockdown was imposed.
A Department of Health and Social Care spokesperson said previously: "Seeing that cases in Leicester were significantly higher than other parts of the country, we make no apology for working with Leicester leaders to take decisive action to reverse this trend and save lives.
"The government's priority is to protect the public, which is why local partners in Leicester have been able to access government-held data from 19 June, and we are working closely with them so that these necessary local restrictions can be removed as soon as possible."