David Cameron has ordered that the photographer Andrew Parsons and camerawoman Nicky Woodhouse be removed from the public payroll after intense criticism about the appointment of his so-called "vanity staff" to the civil service.

Sources in Downing Street said that they stood by the logic of the appointments – that centrally employed media staff could cut the cost of the government's freelance media budget – but that they now acknowledged that the move "sent out the wrong message" when the rest of the public sector was being asked to make savings.

The U-turn means the pairs' salaries of between £36,000 and £44,000 each will be paid for by the Conservative party and they will lose their Cabinet Office desks and return to the party's headquarters at Millbank.

A Downing Street source said: "The PM has decided that Andrew Parsons and Nicky Woodhouse will no longer be paid for by the taxpayer. Their jobs were across government and designed to save money; however, he does feel it sends the wrong message. We will continue to find ways to save money across government communications."

Parsons was Cameron's personal photographer in opposition and was subsequently employed on a short-term contract, which allows new governments to make personal appointments to all ministers. Woodhouse made the Webcameron videos for the Conservative party that featured in its election campaign and was similarly employed to produce short films for all government departments.

Labour's Michael Dugher said he welcomed the prime minister "bowing down to public pressure".

The Labour MP, who raised the issue two weeks ago with the cabinet secretary, Gus O'Donnell, added: "The prime minister should have known from the start that it's wrong to bill the taxpayer for his vanity photographer. But today's flip-flop raises more questions. If it's wrong to charge taxpayers for Andrew Parsons or Nicky Woodhouse then why are so many other Conservative party workers being hired via this sharp practice as so-called civil servants?"

O'Donnell last week wrote to Dugher backing the appointments and confirming that 30 staff were employed on short-term fixed contracts, the majority of which have not previously worked for a political party. Others include Rishi Saha, an internet expert who is close to Cameron's inner circle and was head of digital strategy for the Conservatives, who was appointed deputy director of digital communications at the Cabinet Office.

The Guardian understands that in at least two unnamed cases the Cabinet Office conduct and ethics department was asked to vet the appointments and passed them.