Prime Minister Boris Johnson appeared confused over the rules for single parents living apart from their children during a Covid briefing.
A questioner called Christopher, from Margate, Kent, asked what would happen where one parent lives in a high alert level area and the other medium.
He was told to check the government's website for guidance but that there are restrictions on such movements.
But government advice says there are exceptions for childcare arrangements.
Speaking at Downing Street, Mr Johnson said: "Christopher, I think the guidance alas is that - you should go on the website obviously and check - but when cases go to a higher tier from the basic medium then there are restrictions on household contact.
"So depending on how you define your household you may find there are restrictions, but you really need to go onto the website to find out what's going on in Kent and what's going on in Essex in order to be absolutely sure."
Graphic on measures in the new three-tier system for England
The government advice for both areas in the "high" and "very high" Covid alert level specifies that there are exceptions to travel restrictions where children do not live in the same household as both their parents or guardians.
The regulations state that there is an exception for "the purposes of arrangements for access to, and contact between, parents and children where the children do not live in the same household as their parents or one of their parents".
It comes after an earlier incident, last month, when the prime minister apologised after making a mistake when talking to media about the rule of six in the north-east of England.