It comes as opposition leaders accused Mrs May of showing contempt for Parliament.
Lib Dem leader Sir Vince Cable said the United Kingdom government was doing plenty of planning for a no-deal Brexit, which it did not want but thought possible, but "no planning appears to be taking place for a people's vote which we believe is highly probable".
Liberal Democrat Leader Sir Vince Cable made a similar point in the Commons chamber.
The correspondence stated: "We believe that this deferral shows a contempt for Parliament".
Justine Greening, the former education secretary and one of relatively few Conservative MPs on the government benches for the debate, intervened to stress to Lidington that May's endeavours were not the issue.
Michael Heseltine did in 1976 when he was infuriated that the Labour government had got a vote through and he was accusing them of cheating.
However, some Welsh Labour politicians have urged Mr Corbyn to act.
Speculation had reached fever pitch on Tuesday night that the threshold of 48 letters from Tory MPs calling for a vote of no-confidence in May's leadership had been hit.
They were joined by Labour's Dame Margaret Beckett and Conservative MP Anna Soubry, leading figures from the pro-referendum wings of their parties.
But the shadow Brexit minister, Jenny Chapman, indicated that the no-confidence vote could take place by the end of next week.
The Public Administration and Constitutional Affairs Committee today released a report that said, under that eventuality, that the Prime Minister would be expected to resign unless her "authority could be restored".
It's after Theresa May deferred a crunch vote on her Brexit deal after admitting she did not have enough support to get it through the Commons.
"This is no longer a functioning government and the prime minister must admit her deal is dead".
He said there was "no doubt about her commitment to parliamentary accountability, whatever the cost to her in terms of time".
Earlier, Ogmore MP Chris Elmore called the delay to the vote "ridiculous".
The report stated: "Outside the terms of the Act, if the House were to express no confidence, unless that authority could be restored, the Prime Minister would be expected to give notice that he or she will resign, but only when he or she is in a position to recommend to the Sovereign an alternative person to form a new administration".
Plaid Cymru's leader at Westminster, Liz Saville Roberts, said: "Jeremy Corbyn runs the risk of being seen to condone the chaos for his own possible benefit".