Culture Secretary Oliver Dowden said he could not guarantee that all legal restrictions on social distancing could end in June.
He told the Andrew Marr Show on the BBC: “Of course they could be delayed if the situation worsens, but right now we are on the right track.”
To ensure this is England’s final lockdown, the Cabinet Secretary added, “My entire experience of last year and I think anyone watching last year’s experience cannot rule out.
“But we are confident that we don’t need to have another ban because we did and it is the last thing in the world we want to do.”
Mr Dowden also tried to ensure that vaccination records would not be introduced permanently.
He said, “Of course we would never try to do this permanently. It’s just that it could be a tool in the short term.”
The Minister of Culture also confirmed that the UK currently has no coronavirus vaccine surplus after a report may have been sent to Ireland.
He told Sky’s Sophy Ridge on Sunday: “Our top priority is of course to make sure we deliver vaccines in the UK.
“We clearly don’t have an excess of vaccines right now. Should we get to the point where we have an excess of vaccines, we would make decisions about how to distribute that excess.”