Criticism of how four Covid-19 “tsars” were put in place has been voiced by an independent watchdog, as a new spotlight also fell on appointments of as many as 19 Tory-linked figures over the past 12 months.

“Greater clarity” about the terms on which the four were appointed in areas such as PPE and vaccine procurement “might have helped”, said the head of the public appointments watchdog, who recently expressed concern that the government was presiding over a new wave of political cronyism.

The comments by Peter Riddell, an apolitical figure, came as Labour challenged Britain’s most senior civil servant to provide assurances that proper procedures were being followed in appointments. Nineteen roles have been singled out, including the handing of a Home Office job to a close friend of the prime minister without it being advertised, and controversy over the appointment of the Tory peer James Wharton as chair of the Office for Students (OfS).

The public are being “left to draw their own conclusions from what appears to be a growing network of senior positions appointed because of links to the Conservative party”, according to a letter from Labour sent to the Cabinet Office secretary on Friday.

The challenge by Rachel Reeves, Labour’s frontbench spokesperson on Cabinet Office matters, to “put concerns to bed” comes after alarm bells about political patronage were sounded by the standards watchdog, Jonathan Evans, and Riddell, commissioner for public appointments.

Asked if he felt public perceptions of governance had been dented by the recent controversies, Riddell told the Guardian he had seen no polling, but added: “There has certainly been more social media discussion about alleged ‘cronyism’ – usually from the affected sectors – as well as media queries, and I’m in no way complacent about the risks.”

While recognising the need to respond quickly to the Covid-19 pandemic in appointing a number of tsars in areas such as PPE and vaccine procurement, with normal competitions impractical, he added: “What might have helped is greater clarity about the terms on which people were being appointed.”

He said concerns had been raised over those selected by the government to sit on the panels that appointed people to public roles.

“This normally involves an informal discussion between a department and my office, and this presented hardly any problems until last summer when we had a number of cases where names were suggested which were in breach of the code. In each case, I pointed out the clash and an alternative acceptable name was put forward.”

Riddell said he was reassured that “efforts are being made within Whitehall to ensure that such problems do not happen again” and stressed there were 1,000 public appointments each year and the vast majority were made properly.

The success of Kate Bingham – whose involvement initially raised eyebrows on the basis that she was the wife of a Tory MP – in overseeing the UK’s vaccine taskforce has counteracted some criticism. But allegations of political patronage have been fuelled by recent appointments. They include former Conservative MPs such Wharton and George Hollingbery, whose appointment as ambassador to Cuba raised the ire of civil servant unions.

In others, a link to Johnson has been explicit, such as in the appointment this month of his former aide Edward Lister as Middle East envoy. Nimco Ali, a close friend of the prime minister and his fiancee, was meanwhile given an official position at the Home Office without the role being publicly advertised.

Other appointees who have faced questions include the new children’s commissioner, Rachel de Souza, who was director of a campaign group with connections to Conservative figures including those close to Johnson.

Accusations of cronyism had been prompted last May when two former Conservative MPs, Sir Patrick McLoughlin and Nick de Bois, were appointed to senior tourism jobs despite an apparent lack of direct experience in the sector. Criticism was also levelled at the appointment of the former Tory minister Sarah Newton as chair of the Health and Safety Executive, a move that unions said broke with a practice of having the regulator’s chair come from either a trade union or employer background.

All of the above, and others, are listed in Labour’s letter to Simon Case, the cabinet secretary, which called for the civil service to investigate the appointment of Wharton, a former campaign manager for Johnson, as head of the OfS despite him having no experience of the sector.

Reeves also asked in the letter to Case for clarification on which roles were advertised, where they were advertised, which codes of conduct the roles must abide by, and which of them are required to follow the “Nolan principles” for public life.

Alex Thomas, who was principal private secretary to the late Sir Jeremy Heywood when he was cabinet secretary and head of the civil service, told the Guardian: “Open and fair competition is an important principle when making public appointments. There have been signs that for some appointments the government is trying to subvert the process by stacking panels or briefing out their preferred candidates to dissuade others from applying.”

“That’s not the way to get the best people to do these jobs, which, after all, is what ministers should want,” added Thomas, who now leads work on policymaking and the civil service at the Institute for Government thinktank.

The issue has blown up again ahead of the looming appointment of the former Daily Mail editor Paul Dacre as chair of Ofcom, a move that has been likened to a continuation of a perceived Conservative culture wars “power grab”, after the Tory donor Richard Sharp was named as the new BBC chair and its director generalship went to Tim Davie, a former deputy chair of the Hammersmith and Fulham Conservative party.

A Cabinet Office spokesperson said: “Public appointments are made in accordance with the governance code for public appointments and are regulated by the commissioner for public appointments.

“Political affiliation is not a bar to holding a public appointment so long as the individual acts in the national interest – of the 9% appointed which declare significant political activity in recent years, 36% stated this was on behalf of the Conservative party and 46% on behalf of the Labour party.

“Other appointments are made in accordance with established procedures.”