At least 80 people are presumed to have been killed in the deadly blaze at Grenfell Tower, with United Kingdom police warning it is likely some victims will never be identified and that it could "take until the end of the year" before a final death toll is known.
But Labour wants to force the government to publicly defend public spending cuts, with an eye on the prospect of another election if May can not hold on.
The vote was the first the government faced in Parliament since the June 8 election.More news: 76ers Among 7 Teams Interested In Andre Iguodala
The prime minister said: "The question is... why is it that fire inspections, that local authority inspections, appear to have missed this essential issue?"
Corbyn slammed the "disastrous effects of austerity" and accused the government of continuing to "disregard working-class communities" and of "cutting corners".
There is a link between cuts in local authority expenditure and the level of building control, inspections that have taken place and therefore the safety of the residents in those towers.
May has come under fire from inside and outside her Conservative party over her strategy for Britain's departure from the European Union and has been forced to scrap many of her planned reforms.
Labour tabled an amendment on Wednesday to the Queen's Speech - the government's legislative agenda - calling for an end to the pay cap and cuts to the police and fire service budgets.More news: Iraqi military says it has retaken two Mosul neighborhoods from Islamic State
After the terms of the deal between the government and the D.U.P. were made public on Monday, Corbyn denounced the agreement as not "in the national interest, but in the interest of Theresa May and the Conservatives' own political survival".
May's party is now in negotiations with Northern Ireland's DUP to secure an informal parliamentary deal that would give it an effective majority.
The Democratic Unionists have agreed to support the Tories on key votes.
Opposition parties and devolved administrations in Scotland and Wales have called on the Government to match the funding boost for Northern Ireland across the United Kingdom, with shadow chancellor John McDonnell calling for an end to austerity "throughout the UK", not just in the province.
Theresa May's election gamble backfired, resulting in the Conservative party losing their majority of seats.More news: Dashcam Video of the Philando Castile Shooting Just Released
A vote on the amendment is due to go ahead on Wednesday at around 7 p.m. local time.
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