The latest lockdown has raised the possibility of elections due on 6 May being postponed, some of which are already delayed from May 2020.
Voting is due for the Scottish Parliament, Welsh Senedd, the mayor of London, English county councils and various other English local elections and elected mayoralties.
Local Government Minister Luke Hall is understood to have told councillors in an online briefing this week that there are no plans to postpone the May 2021 elections.
He said guidance would be developed on delivering elections in pandemic conditions.
The County Councils Network has demanded clarity on whether the elections will proceed.
Its chair David Williams, the Conservative leads of Hertfordshire County Council, said: “The elections in county areas this spring are the single biggest type of council elections scheduled to take place this year: with up to 19 million people potentially eligible to vote in 32 different areas.
“These are substantive logistical undertakings at any time for unitary, county and district councils, but the pandemic creates significant challenges to ensure votes can be cast safely.”
He added: “Continuing speculation about the elections being deferred is unhelpful so we need urgent clarity and a swift decision from the government as soon as possible on whether these elections take place as scheduled.”
In Wales the Senedd has powers to postpone elections if necessary and last November said the elections should be held but with an early drive to encourage postal vote applications,
A Senedd report noted First Minister Mark Drakeford has said it was “not right that this Senedd should be extended beyond its current term” and that it needed “a democratic refresh”.
But he said that it would be irresponsible of the Welsh Government “not to make plans in case the pandemic is so serious in May of next year where it wouldn’t be safe to hold an election.”
Mr Drakeford told the BBC this week: "I remain committed to a Senedd election in May of this year.
"But in the circumstances we face it is simply responsible to put on the statute book a bill that would allow some flexibility in that date should that be necessary and we'll embark on that process early in the coming term.”
The Scottish General Election (Coronavirus) Bill provides powers to decide if the election must be postponed for up to six months and to hold an all-postal election or with polling over multiple days.