Boris Johnson and Rishi Sunak have rejected calls to resign, despite being fined by police for breaking lockdown rules in Downing Street in June 2020.
The prime minister, the chancellor and the PM's wife all received fixed penalty notices for attending a birthday gathering for the PM in No 10.
As a result, Mr Johnson became the UK's first serving prime minister to be sanctioned for breaking the law.
All three apologised, but opposition MPs say the PM and Mr Sunak must quit.
Mr Johnson said he felt "an even greater sense of obligation to deliver", while the chancellor said he was "focused on delivering for the British people".
But a group representing bereaved families said there was "simply no way" either could continue in their jobs, calling their actions "truly shameless".
Amanda McEgan, whose daughter Isabel died during the pandemic, said the prime minister's conduct during the lockdowns made restrictions on the 19-year-old's funeral "more hurtful".
Opposition parties accused Mr Johnson and Mr Sunak of lying to the public about their attendance at the Downing Street gathering, with Labour leader Sir Keir Starmer and the first ministers of Scotland and Wales demanding they step down.
The SNP and the Liberal Democrats also led calls for Parliament to return from its Easter break so the PM and chancellor could face questions from MPs.
Nearly all cabinet ministers have publicly backed Mr Johnson and Mr Sunak - including Foreign Secretary Liz Truss, who said they were "delivering for Britain on many fronts".
Nigel Mills is currently the only Tory MP known to have said publicly that Mr Johnson should go, telling BBC Radio Derby: "I don't think his position is tenable".
Others who called for him to resign earlier in the year, including Scottish Tory leader Douglas Ross, have now said they don't think he should.
Transport Secretary Grant Shapps said Mr Johnson was "mortified" about being fined, but argued he had not "set out with malice to break the law".
He told BBC Breakfast he understood public anger over the parties, but added: "Everyone is human. People make mistakes".
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