He was, he said, "deeply concerned about the spiraling costs" of renewal, said that a nuclear deterrent was not the best response to new threats such as that posed by the Islamic State militant group (ISIS), and urged the government to "step up to the plate and promote rapid nuclear disarmament" internationally.
Opponents say the vote is being used by the newly appointed May to unify her party after a bruising Brexit campaign and embarrass Labour by highlighting its own deep divisions.
Theresa May without hesitation said that she would be willing to press the nuclear button - without flinching in the face of that question, there was not a moment's doubt.
Speaking during her first appearance at the despatch box as prime minister, Mrs May said it would be irresponsible not to renew the four nuclear-armed submarines which take turns to patrol the North Atlantic.
Former defence minister Kevan Jones asked Mr Corbyn: "You, like me, stood in May 2015 on a party policy - agreed at our conference through our mechanisms in the party - for the renewal of continuous-at-sea deterrent.
The very existence of nuclear weapons is an affront to and a theft from the poor and vulnerable of our world", said Pat Gaffney, general secretary of Catholic peace movement Pax Christi at a gathering attended by faith groups, students and scientists outside of parliament on Monday evening.
She insisted it would be an "act of gross irresponsibility" should the government discard the Trident weapons system, as she led calls to replace the submarine fleet which carries the missiles.
Corbyn, who supports scrapping Trident, allowed Labour MPs a free vote on the issue.
Labour's foreign and defence spokespersons said they would abstain on the vote but numerous backbench Labour MPs took to the floor to criticise their leader's stance.
Labour MP Toby Perkins, who last month resigned as shadow armed forces minister, compared Labour frontbench opposition to Trident with the arguments "of a 13-year-old".
"But as long as nuclear weapons exist, it will unfortunately remain a nuclear alliance".
The Scottish National Party, which holds 54 of the 650 House of Commons seats, was firmly opposed to renewing the Trident fleet, which is based on Scotland's west coast.
The missiles are carried on four submarines based in Scotland.
"Is she personally prepared to authorise a nuclear strike that could kill 100 thousand innocent men women and children?"
And former United Nations weapons inspector Hans Blix said he could not see "how the UK would be any more protected if it extended the life" of Trident.