Pubs may have to shut to allow schools to safely reopen if the NHS Test and Trace system is not "fixed urgently", the Greater Manchester mayor has said.
Only 53% of people in contact with a coronavirus carrier have been traced in the area, according to data.
Mayor Andy Burnham said: "There is a growing amount of evidence that pubs are one of the main places where this virus spreads."
The BBC has asked the government for a response.
Following a rise in infections, residents in parts of northern England including Greater Manchester have been banned from mixing with other households - apart from those in their support bubbles - in areas such as homes, pubs and private gardens.
Pubs are allowed to remain open, however, with different support bubbles banned from mixing.
Mr Burnham joined calls for the government to improve the contact-tracing system, saying its tracing rate in Greater Manchester was "nowhere near good enough".
He told BBC Radio 5 Live: "You can't safely open schools with pubs open as well, with that level of performance."
Earlier this month, Prof Chris Bonell from the London School of Hygiene and Tropical Medicine estimated only half of contacts were being traced in England, adding the system was "not achieving the levels we have modelled".
However Local Government Minister Simon Clarke said their figures were higher.
On Sunday, Prime Minister Boris Johnson said there was a "moral duty" to get all children back into England's schools in September.
Mr Burnham said some councils had shut pubs recently after "a substantial minority" broke rules.
He joined calls from other regions for "more direct powers" to close venues that were flouting regulations.
The mayor said: "This NHS test-and-trace system currently is not good enough to go into a winter with no treatment or vaccine, and the sad thing is it'll be our poorest communities that are most exposed.
"We have got August to fix this test-and-trace system… and if we haven't then I think there is a real possibility that we will have to close the pubs."
He repeated calls for government to listen more to regional authorities, urging ministers to give councils extra funds to do more contact tracing locally, including for "people who can knock on doors and do a better job than this national call centre system".
Earlier this week, Blackburn's public health director said the national system was "not fast enough", and authorities in the town said they were "already seeing benefits" after launching a tracing system where council staff used local knowledge.