Parliament’s ethics watchdog has been urged to investigate Boris Johnson’s Downing Street finances in the wake of this week’s sleaze scandal, as Kathryn Stone was said to be undeterred by government attempts to undermine her.

Angela Rayner, Labour’s deputy leader, called on Stone, the parliamentary standards commissioner, to open a new investigation into the refurbishment of the prime ministerial flat, which reportedly cost GBP200,000 and was initially funded by a Tory donor.

It comes after the government attempted to overthrow a ruling by Stone in relation to lobbying by the Tory MP Owen Paterson. Ministers also tried to overhaul the system designed to crack down on sleaze. Rayner accused the prime minister of trying to install a “sham group of Tory stooges who would do his bidding”.

On Friday Johnson threw down the gauntlet to Stone by refusing to declare the costs of his Marbella holiday last month, which was funded by the family of the Tory peer and minister Zac Goldsmith.

Amid growing anger over the sleaze debacle, a Conservative former member of the standards committee said it was “quite convenient” timing for Johnson to be trying to “trash the existing disciplinary system” in an attempt to escape scrutiny of his own actions.

Stone has said she will decide whether to investigate the refurbishment of No 11 Downing Street once the Electoral Commission has completed its own investigation. The commission is understood to have completed its inquiry and has handed a draft of its findings to the Conservative party.

Allies of Stone regard this week’s chaotic events in parliament as part of an attempt to undermine her authority, but two sources told the Guardian she was undeterred and would continue to take a robust approach to investigating MPs’ conduct. On Wednesday she released a statement saying she intended to remain in post until the end of her term in December 2022.

Rayner said in a letter to Stone on Friday that Johnson’s behaviour this week in trying to shield Paterson by changing the standards system “demonstrates that the prime minister is clearly attempting to disempower the role of the parliamentary commissioner for standards and even remove you from your post at a time when he is facing a potential investigation by you for breaching the rules yet again”.

She added: “This situation is deeply concerning for all of us who believe in democracy and basic standards of decency, integrity and honesty in public life. This situation also makes it all the more important that you are able to carry out your investigation into whether the prime minister broke the rules in relation to the financing of the refurbishment of his Downing Street flat, just as he broke the rules on a number of occasions in the past.”

Rayner said the government-backed attempt to overhaul the standards system by creating a new committee chaired by a Tory MP was an attempt to “make Conservative MPs judge and jury over allegations of corruption and rule-breaking”, adding it was a “blatant attempt” to prevent the Stone from investigating him.

Dominic Grieve, a former Tory member of the standards committee, said Johnson’s intervention “clearly could only be interpreted on the basis that he intended to rubbish the committee and the commissioner and undermine them”.

He added: “What this group of ministers – led by this prime minister – have done is to say this is a chum whom we are going to help. And in doing so it doesn’t matter if we trash the existing disciplinary system, which leaves it in tatters for the future. And it just so happens that at the same time, well, that might be quite convenient, because the prime minister himself might be the subject of its scrutiny shortly over his issues of non-declaration.”

The question of whether the government is trying to oust Stone was underlined when Conservative headquarters issued guidance to Tory MPs on how to answer the question about whether she should resign. It did not tell them to disagree but only to say changes to the standards system were “about strengthening the process more broadly”.

Sir Malcolm Rifkind, a Tory grandee and former chair of the standards and privileges committee, told the Guardian he was “genuinely worried” the Conservatives’ reputation was being “seriously being damaged by events of this kind”.

He said Downing Street should confess it “got it wrong” and “show some contrition given the way they’ve used the power they have got has not been in the best public interest and won’t happen again”. He added: “They’ve got to show that they’re learning from experience, that this is not the way either to treat the House of Commons or the country as a whole. The reputation of the government will not just be temporarily but potentially permanently damaged, if the public assume that this kind of behaviour was going to continue every so often.”

Downing Street declined to rule out the possibility Johnson could nominate Paterson for a peerage despite the former MP being found to have committed an “egregious” breach of parliamentary rules on paid lobbying.