Schools in England and Wales could remain closed until after Easter, the UK's education secretary, Matt Hancock has suggested with returns before no more than a "hope".
In an interview on the BBC's Andrew Marr Show, Mr Hancock would not commit to dates for schools to fully reopen.
"We're really clear we want to get schools back and as safe as we can, but we have to watch the data...
Of course I hope schools go back after Easter and the vaccination programme is going fast. But we've got to make sure that we get the cases down and we've got to protect the country from new variants coming in from abroad."
Earlier Mr Williamson had signalled pupils could be told in a week's time if they would be returning to classrooms after the February half-term.
Appearing on Sky News, Mr Williamson said his Department for Education would "want to give all schools a clear two weeks' notice period" ahead of their full reopening.
Separately, the "debate" as to whether vaccinations for all school staff should wait until the most clinically vulnerable groups have received their inoculations, told the BBC.