Parliament is to close for Easter a week early amid fears that coronavirus has been spreading fast through Westminster.

Jacob Rees-Mogg, the leader of the House of Commons, laid a motion saying parliament will adjourn on Wednesday night until 21 April, but that the date would be reviewed closer to the time and there are a number of suggestions it may return for only two days a week with limited numbers.

MPs have called for ministers to take part in daily video conferencing so they can keep scrutinising the government’s handling of the Covid-19 outbreak while parliament is in recess.

The Labour backbencher Wes Streeting said: “The idea we are sending parliament away during a national crisis, rather than scrutinising the government effectively, will lead to concerns from the public.

“At a time when we are asking key workers to, and the public sector and private sector to go to work, I think that parliamentary scrutiny is an essential function when we are being inundated with constituents who are self-employed, people on statutory sick pay struggling to make ends meet or stuck abroad.”

The former minister Chris Bryant MP said: “MPs should be allowed to ask questions like journalists are. If Rishi Sunak is making a statement on support for the self-employed you should allow MPs to ask questions as well. There is no reason why this couldn’t be set up with video conferencing.”

Under questioning from MPs on the last day before recess, Rees-Mogg said he was liaising on the creation of hotlines for MPs into ministries so they could seek urgent response to coronavirus-related issues during the break.

Both Streeting and Bryant also suggested now could be the time to implement electronic voting, a move that the European parliament made on Monday. Although few votes are expected, Streeting said: “This is not necessarily a permanent way of running our democracy but extraordinary times call for extraordinary measures.”

Parliamentary authorities are considering opening for two days a week after the Easter break, likely to be a Tuesday or Wednesday, with a representative proportion of the political makeup of the Commons.

Bryant suggested using Westminster Hall on the parliamentary estate to house the Commons after Easter. As one of the largest medieval halls in Europe, it could easily host 650 MPs with distance between people, he suggested.

A Whitehall source said a range of plans were being considered, adding: “The plans have to be flexible because if we’re in a Italy situation in a few weeks’ time we will need a different plan to if we’re in a South Korea situation.”

The Liberal Democrats chief whip, Alistair Carmichael, said he was having talks with his government counterpart over ways to allow parliamentary scrutiny of government after the Easter recess without all MPs having to be in Westminster.

Carmichael, the MP for Orkney and Shetland, said his revamped, physically distanced trip back to his constituency – a sleeper train to Edinburgh, a hire car to Aberdeen then a solo cabin on the ferry to Orkney – took 26 hours each way.

“This is fine to get me home at the start of a recess, but if this were to be the regular pattern, I can’t spend 52 hours a week doing this, every week. We need to find a more creative and inventive way of doing it,” he said.

With a vote needed on a finance bill next month, Carmichael said, one option could be to only call back a proportional sample of MPs from each party, totalling 100 or fewer.

A way to ensure scrutiny could be to hold events via video link, and to create a cross-party select committee, as New Zealand has just done, where the new body is chaired by the country’s leader of the opposition, Simon Bridges.

Talks so far with the government chief whip, Mark Spencer, had focused on pairing MPs to mean not all had to come into Westminster, Carmichael said: “Whether they are prepared to go as far as the New Zealand example, I think they will need some persuasion, but after four or five weeks with no parliamentary scrutiny, I think there will be a head of steam in the country for parliament to do more than just nod stuff through.”

Robert Jenrick, the communities secretary, was challenged on whether the adjournment would prevent proper scrutiny of the government’s coronavirus response, after speculation that parliament could end up being shuttered for months.

Jenrick insisted parliament would return after Easter as usual, potentially with some changes such as committee meetings held remotely.

“It will return in the usual way so MPs can continue to hold the government to account. We live in a democracy so it is absolutely essential the government is held to account particularly in times like this. Parliament will return,” he said.

“There has been another order in parliament to create ways for select committees to operate remotely. Innovation will happen to make it possible for MPs to hold us to account and that is absolutely right.”

At least 20 MPs are confirmed or suspected to have had coronavirus, and No 10 officials, members of parliamentary staff and political journalists are also among those who are isolating.

The first confirmed case among MPs was Nadine Dorries, who has since returned to work as a health minister.

Parliament has continued sitting with some changes to voting to ensure that MPs are not crowding into lobbies together but keeping their distance. It broke tonight for Easter one week earlier than scheduled.