After the result in the Commons, shadow Brexit spokesman Matthew Pennycook appeared to suggest the party is ready to act, tweeting it is "now time to wholeheartedly get behind efforts to facilitate a new public vote that includes the option of staying in the EU".
The Hackney North motion, backed by members of the local party by 45 votes to 35, said: "It is unacceptable to allow our representatives to slander the party and its members whilst we put them into office".
Mr Corbyn has come under pressure from the Labour ranks to throw the party's full weight behind a second referendum.
"Then if that fails, rather than a bad deal or a no deal Brexit, we must return the decision to the British people".
"We will also continue to push for the other available options to prevent those outcomes, including a close economic relationship based on our credible alternative plan or a general election". More MPs are potentially expected to leave Labour within the next few weeks.
Locally, 60% of Rochdale voters opted to leave.
After months of saying that Britain must leave the European Union on time on March 29, May opened up the possibility on Tuesday of a short limited extension to the exit date.
The Prime Minister confirmed in her latest Brexit statement today that the second meaningful vote on her deal has been delayed, and will be held not this week but instead at some point before 12th March.
Trump extends China tariff deadline after 'substantial' progress
In retrospect, the bilateral meetings in Beijing prior to last week's talks in Washington were "critically important", he said. US tariffs on $200 billion of Chinese goods had been scheduled to rise to 25 percent from 10 percent at 12:01 a.m.
An amendment tabled by Labour's Yvette Cooper, created to pin the PM down by placing her promise in a motion approved by Parliament, was passed by a majority of 482 - with 20 Tory hardliners opposing it.
The government accepted two of the amendments including one by Labor MP Yvette Cooper to lock May to a commitment made to MPs on Tuesday, including one which will allow parliament to delay Brexit if her deal is rejected when a meaningful vote takes place next month. Mr Watson said Labour was "perilously close" to losing new MPs after nine walked last week to join breakaway The Independent Group (TIG).
In an earlier vote of 240 against 323, a majority of 83, Britain's main opposition party lost what was one of its top Brexit demands, keeping Britain in the European Customs Union along with alignment to the EU single market.
Labour activists in two constituencies have criticised "right wing" Labour MPs amid the party's anti-Semitism row.
Mr Corbyn's plan was supported in Wednesday night's vote by Conservative former chancellor Kenneth Clarke and Liberal Democrat deputy leader Jo Swinson - who backed the plan accidentally.
Lawmakers also rejected a proposal on Wednesday by the Scottish National Party calling for no-deal Brexit to be ruled out under any circumstances.
May's government faced a number of backbench attempts to seize control of the Brexit process with five amendments tabled on a motion to move forward with Brexit.
But Labour said he had effectively been sacked.