Number 10 rejects Ofsted chair's claims it is ousting non-Tories from key posts
Downing Street has said it makes appointments "on merit", following claims Number 10 is ousting non-Tory supporters from public posts.
Baroness Morgan, the outgoing chair of Ofsted, said she was the victim of a "determined effort from Number 10" to appoint more Tories.
The Labour peer said her removal - from the autumn - was part of a "pattern".
Lib Dem schools minister David Laws is said to be "furious" about the decision to replace her.
Downing Street said the decision not to renew her term of office was made by Education Secretary Michael Gove.
A Number 10 spokesman said: "Michael Gove has thanked Sally Morgan for her effective and long service as chair of Ofsted.
"The decision not to reappoint her was his decision.
"This government appoints people on merit: for example, Sally Morgan was herself appointed under this government; and the former Labour adviser Simon Stevens is about to take up the post of Chief Executive of NHS England.
"We have also asked former Labour cabinet ministers to carry out independent reviews on key public policy issues, including Alan Milburn on social mobility and John Hutton on public service pensions."
The statement was made following the claims made by Baroness Morgan, who was appointed by the coalition in 2010 as chair of the education inspectorate for England.
A source close to Mr Laws told the BBC: "David is absolutely furious at the blatant attempts by the Tories to politicise Ofsted.
"The decision to get rid of Sally Morgan had absolutely nothing to do with her abilities, or even education policy, and everything to do with Michael Gove's desire to get his own people on board.
"David Laws is absolutely determined not to let Michael undermine the independence of this vital part of the education system.
"David's primary concern now is not to let Conservative game-playing destabilise Ofsted and he'll be working closely with them as schools minister to make sure that doesn't happen."
A senior Lib Dem source accused Mr Gove of attempting to "reward Tory cronies".
Baroness Morgan said her removal was part of a pattern which had seen a series of non-Conservative supporters on bodies like the Arts Council and the Charity Commission replaced with loyal Tories.
She said the impetus behind the appointments appeared to come from No 10.
"I really do think it's just I am the latest of a fairly long list of people now who are non-Conservative supporters who are not being re-appointed," she said.
She said she believed the move was not specifically against Labour, but against those who did not support the Conservatives, and added: "I think there's a lot of concern about it.
"Often they are people who have been working really well with their organisations and, indeed, with their host departments, so I do think this is coming from Number 10.
"I don't think it is coming from individual departments."
Baroness Morgan told Radio 4 the issue needed to be looked at by the cabinet secretary, the most senior civil servant, and the Cabinet Office.
"One of the really important things about public appointments is that they are made on the basis of merit and they are seen to be transparently made," she said. "I think there's something going on in the centre that's mitigating against that."
Education Secretary Michael Gove has not commented on allegations in the Independent he was dismissing Baroness Morgan but praised her contribution.
Mr Gove said: "She has brought great knowledge and insight, leading the board strongly through a period of significant change, both managing the smooth transition when there were changes in chief inspector, and leading the reforms to the inspectorate and its work.
"I hope that she continues to play an active role in helping to shape the education landscape to improve standards for all children and young people."
'Lack of plurality'
This comes days after the education secretary denied claims by Sir Michael Wilshaw, the chief inspector of schools in England, that the Department for Education had briefed against Ofsted.
Shadow education secretary Tristram Hunt told the BBC: "I think the prime minister has a particular problem with women in public life from non-Conservative backgrounds."
Mr Hunt said the Conservative party had shown "a worrying lack of plurality in public appointments".
He added: "Downing Street are very keen to get their own people onto public boards and the secretary of state for education should have stood up for Sally Morgan.
"He should have stood up for a good public appointment rather than give in to party political games from Downing Street."
In a statement, Ofsted said Baroness Morgan's term of office "has been extended until the autumn of 2014 by the secretary of state while the process is put in place to find a successor".
The Independent also reported that Deputy Prime Minister Nick Clegg had complained to the cabinet secretary about Conservatives making "party political" appointments.