More than 100 MPs have signed an open letter calling for the creation a digital Parliament.
The group of MPs from Labour, the Lib Dems and the SNP say that during the "exceptional circumstances" of the coronavirus outbreak "Parliament must work exceptionally".
Parliament is closed until 21 April at the earliest, after concerns were raised about spreading the virus.
The PM tested positive for COVID-19, and a number of MPs are self-isolating.
In the letter to the Clerk of the House of Commons, the MPs say "it is clear that Westminster is not a safe working environment and cannot be made so whilst including a representative number of MPs".
With the nation told to #StayHomesavelive MPs must lead by example with a #DigitalParliament enabling #SocialDistancing Democracy. Over 100 MPs have joined me in asking the Clerk of the House of Commons to move Parliament online for the duration of the #coronavirus crisis pic.twitter.com/5U4e5MWSZd— chi onwurah (@ChiOnwurah) March 31, 2020
The letter adds: "We must lead by example.
"Though changes comes slowly to Parliament, in this time of crisis we urge you to work with the Parliamentary Digital Services to design a digital Parliament in which all members can participate."
The MPs say that given the urgency of the task, "off-the-shelf solutions" will be required, and that a new system may initially be "rough and ready".
The letter adds: "People up and down the country have made huge behavioural changes in a matter of days and we must show we are capable of it too."
Announcing the extended Commons recess last week, Speaker Sir Lindsay Hoyle said work was under way to give MPs the technology they need to stay connected during the break, including the possibility of "virtual parliament and virtual select committees".
The Parliamentary authorities have faced several calls for electronic voting to be introduced in recent years, along the lines of the systems used in the European Parliament or the Scottish Parliament, or even to allow MPs to vote remotely, through secure servers.
At the moment, MPs at Westminster can only pass laws by queuing up in the lobbies behind the Commons chamber to cast their votes. Bells ring across the Parliamentary estate summoning members to take part in votes.
Traditionalists have argued that voting is an important part of being an MP and one of the few opportunities backbenchers get to rub shoulders with ministers - but the current crisis may force a rethink.
The Commons authorities said extra IT capacity would be made available to help select committees continue to do their work while Parliament was not officially sitting and to help them adapt to "new ways of working".
"The House has shown great ingenuity in seeking to continue its business," the Commons Procedure and Administration committees said in a joint statement.
"The temporary procedures and practices put in place in the Chamber and select committees will last as long as the current health emergency demands.
"Looking ahead, as the House and the country it serves return to normal, the experience of these temporary measures will indicate some areas where our procedures, and services to MPs and the public, can be improved."
The prime minister chaired the weekly cabinet meeting in Downing Street via video conference on Tuesday.
Ministers dialled in to the meeting instead of sitting around the cabinet table in Number 10 as part of social distancing measures to curb the spread of coronavirus.
The National Assembly for Wales - or the Senedd - is due to hold an emergency online session on Wednesday in what it says will be the first "virtual" meeting of its kind.