MPs in Cornwall and Devon who are government ministers intend to stay in post after Rishi Sunak and Sajid Javid resigned from the cabinet.
Cornwall MP and Environment Minister George Eustice confirmed to the BBC there was "no change" in his position.
Devon MP and Home Office minister Kevin Foster is "not planning" to resign.
Another Devon MP has called for a general election, while a Cornwall MP said he thought Prime Minister Boris Johnson would try to stay in post.
None of these resigning Cabinet Ministers should get a smidgen of credit. They’ve propped up a disgraced leader for far too long, while all the huge challenges facing Britain have been neglected. The whole of the Tory Augean stables need clearing out. We need a general election.— Ben Bradshaw (@BenPBradshaw) July 5, 2022
In his resignation letter to Mr Johnson, Chancellor Mr Sunak left the Cabinet, saying the public expected "government to be conducted properly, competently and seriously".
Health Secretary Mr Javid told Mr Johnson he was leaving his role as he could "no longer, in good conscience, continue serving in this government".
Mr Eustice and Mr Foster made no further comments to the BBC about their posts or the cabinet members' resignations.
On social media, Totnes MP Anthony Mangnall, a Conservative, called for changes, just over an hour before the first resignation - Mr Javid's.
Mr Mangnall said it was "time for Cabinet colleagues to recognise the damage the PM is doing to the party, the government and the country".
It is time for cabinet colleagues to recognise the appalling damage that the Prime Minister is doing to the party, government and country.— Anthony Mangnall MP (@AnthonyMangnal1) July 5, 2022
It isn’t good enough and each day that passes those who sit in cabinet will be more complicit with this farcical situation.
After the cabinet members quit, Exeter's Labour MP, Ben Bradshaw, said on Twitter that none of the resigning ministers "should get a smidgen of credit", saying they had "propped up a disgraced leader for far too long, while all the huge challenges facing Britain have been neglected".
He called for a general election.
Conservative MP for St Ives Derek Thomas told the BBC Mr Johnson could think about leaving Downing Street and having an "easier life" after his recent no-confidence vote and senior members of the cabinet resigning.
He added: "But, ultimately, it's up to him, and it's up to him how he wants to progress; and I'd imagine he still feels that there's still work he can do."