Boris Johnson won the backing of Tory MPs in Monday evening’s vote, despite a sizeable revolt against his leadership.
The Prime Minister’s legitimacy and authority have been “fundamentally damaged” after his confidence vote victory, Alliance Party MP Stephen Farry has said.
But North Down MP Mr Farry tweeted that Mr Johnson now “needs to resign”.
He added: “Leaving aside his bad policies, he never had the values or character suitable to be Prime Minister.
“With this confidence vote, his legitimacy and authority is fundamentally damaged.”
SDLP leader Colum Eastwood said Mr Johnson had now lost his political authority.
The Foyle MP tweeted: “More than 40% of Tory MPs voted against Boris Johnson.
“He lost any moral authority he had months ago, now he’s lost political authority.
“He should just go.”
The confidence vote result came after Sinn Fein’s Stormont leader Michelle O’Neill warned that political stability in Northern Ireland cannot be held hostage over infighting within the Conservative Party.
Ms O’Neill said the turmoil within Prime Minister Boris Johnson’s party was having an impact on the public in the region.
There has been expectation that a Government bill to override aspects of the contentious Northern Ireland Protocol will be published this week.
Critics of Mr Johnson claim the aim of the bill is more about shoring up support for his leadership among the hard line Brexiteer wing of his party, rather than its stated purpose of achieving greater consensus within Northern Ireland for the post-Brexit trading arrangements.
Powersharing at Stormont is on ice after the DUP refused to re-establish a devolved executive following last month’s Assembly election in protest at the protocol, which has created economic barriers on trade between Great Britain and Northern Ireland.
Ahead of Monday’s vote, Ms O’Neill tweeted: “Our political stability cannot be a hostage to Tory in-fighting.
“This and DUP boycott of Government is hurting the public at a time when we should have their backs.
“Boris Johnson’s threat to Protocol is to risk their entire agreement with EU on withdrawal & with colossal impact.”
The DUP has said that the leadership is a matter for Conservative MPs and they are focused on dealing with the protocol.
Reacting to Monday’s vote, a DUP spokesman said: “The leadership of the Conservative Party is a matter for Conservative MPs.
“Our focus is on freeing NI from the Protocol which threatens our place in the United Kingdom, endangers jobs for our people, drives up costs for customers and reduces choice on our shelves.”
Speaking earlier, the party’s Agriculture Minister Edwin Poots has said that a sizeable rebellion against the Prime Minister could have an impact on the proposed legislation to unilaterally scrap parts of the protocol.
“Obviously if there’s a large rebellion against the Prime Minister that may have an impact,” he told the PA news agency.