Robert Jenrick, asked on Times Radio whether the Government would look to close pubs in such an event, said: "We don't have any plans to do that."
He also said schools would definitely return to full capacity in September and confirmed it would be the priority should there be a second spike of infections.
"I think you're right to say that reopening schools and getting our children back into the classroom with that direct face-to-face contact with their teachers will be a priority for the Government when we have to make those tough choices," he said.
Mr Jenrick said that any fresh restrictions were unlikely to apply wholesale, adding: "We don't want to do anything that is a blanket approach across the country.
Drugs cost 14 lives in South Tyneside
More than 30 new covid cases in South Tyneside but no more virus-related deaths
'Thousands' may have long Covid in South Tyne
11 destinations you can fly to from Newcastle Airport during half-term holidays
Lockdown sparks rise in noisy neighbour complaints
"Our strategy is to manage this in a localised way with targeted action as we've done in Leicester, as we're doing now in the north-west.
"We will follow the data and look at options if we have to but that approach is the way we restrict in certain areas - it is difficult for those who live there but it provides greater freedom for the rest of the country, for businesses to reopen and for people to get on with their daily lives, and that has to be the way forward if we can."