The mayor for the Sheffield City Region calls it the "responsible route" to stem the spread of Covid-19.
A government adviser gave MPs his view during evidence on lessons learned from the pandemic.
The journalist, best known for his 1995 interview with Princess Diana, has complications from the virus.
The two chief negotiators for a post-Brexit trade deal spoke on the phone earlier on Wednesday.
MPs voted against a proposal to extend free school meals over the school holidays until Easter 2021.