John Martin McDonnell is a British Labour Party politician who was appointed the Shadow Chancellor of the Exchequer in September 2015. He has been the Member of Parliament for Hayes and Harlington since the 1997 general election.
MPs who cannot attend Parliament for age or medical reasons will be able to question the government remotely but not vote, says Jacob Rees-Mogg.
The Leader of the House said he would lay a motion to be voted on this Wednesday, ensuring some virtual proceedings can continue for the group.
But critics say the move would still be "discriminatory" against those unable to attend for other reasons.
It comes as MPs passed a motion for a return to a physical parliament.
The plan - meaning all proceedings would go ahead in person, rather than the "hybrid" virtual system Parliament has been using since mid-April - will be in place until 7 July and empowers the Speaker to come up with a physical voting method that respects health and safety guidance from Public Health England.
It has been strongly criticised by MPs from all sides of the House, who warn it would exclude vulnerable MPs and those with caring responsibilities.
But Mr Rees-Mogg said: "What was acceptable for a few short weeks would have proved unsustainable if we had allowed the hybrid proceedings to continue.
"This House plays a invaluable role in holding the government to account and debating legislation which can only properly be fulfilled when members are here in person. "
The cross-party Procedure Committee tabled an amendment to the government's plan to enable the Commons Speaker to authorise electronic voting and allow MPs unable to get to the chamber to participate "digitally".
After Mr Rees-Mogg announced Wednesday's motion, which would allow some MPs to ask urgent questions and take part in statements virtually, the committee's chair, Tory MP Karen Bradley, dropped the amendment.
She still pushed ahead with another, calling for remote voting to be allowed - but it failed to pass by 57 votes.
MPs then voted on the government's plan, which passed by 261 votes to 163.'Unsafe'
During the votes, members had to queue up outside the Commons chamber to observe social distancing, before walking to the Speaker's chair to say their name and which way they were voting.
The vote on Ms Bradley's amendment took 46 minutes - compared to the usual time of around 15 minutes before social distancing measures were brought in.
The vote on the government's plan took 36 minutes.
Some MPs posted pictures of the queue outside the building or in Portcullis House - a building opposite the Houses of Parliament where many MPs' offices are located.
Labour MP Alex Davies-Jones said the way the vote took place had made her "angry", telling the BBC: "The whole voting system has completely fallen apart. It's ridiculous, dangerous and unsafe.
"If I haven't already had Covid then I'm now resigned to the fact that I definitely will. "
The so-called hybrid proceedings have been in place since mid-April, enabling MPs to join proceedings over Zoom via screens in the chamber, and to take part in votes online.
The measures were initially due to end on 12 May, but MPs agreed to a motion from the government to extend them until 21 May - the start of the Whitsun recess.
While a number of MPs welcomed the adjustment to the government's plan made by Mr Rees-Mogg - which may be voted on on Wednesday - many said it did not go far enough.
Labour's shadow leader of the House, Valarie Vaz said the government's plan was "discriminatory".
She added: "I don't know if the leader is living in another universe but the pandemic is still going on. It is not right, or just, or fair. "
The SNP's Westminster leader Ian Blackford said allowing remote access to MPs unable to get to the chamber was "about the rights of all members… and our responsibility to make sure all our constituents are not disenfranchised".
"I do have to ask the question why were we forced to come here today," he added. "The government's official line was if you could work from home then you should.
"Well, we can work from home, we should work from home, because that's the right thing to do - not just for Parliament, but for our family, our colleagues and our constituents. "
Earlier, Tory MP Robert Halfon, who has been shielding at home, told BBC News that scrapping virtual proceedings was "democratically unjust" for MPs who could not return to Parliament, leaving them as "parliamentary eunuchs".
He added: "This stern and unbending attitude of the powers that be is unfortunately why many people sometimes have problems with the Conservative Party. "