The coalition government was engulfed in a vitriolic public row over education on Saturday as the Liberal Democrat schools minister accused his boss, Tory education secretary Michael Gove, of a "blatant" attempt to politicise the independent schools inspection body, Ofsted.

The intervention by David Laws, a close ally of Lib Dem leader Nick Clegg, came after it emerged that Gove had sacked Labour peer Baroness Sally Morgan as chair of the schools inspectorate.

A source close to Laws issued a statement expressing the minister's fury at Gove's move and making clear that the Lib Dems would do all in their power to block actions that they believed would jeopardise Ofsted's independence.

The source said: "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."

The row follows a broadside last weekend by the chief inspector of schools and Ofsted's leading figure, Sir Michael Wilshaw, who broke cover to accuse education department officials of briefing against his organisation. Gove acted swiftly to patch up the rift, insisting that none of his officials had briefed against Wilshaw and praised him for his "superb" work.

But the decision to oust Morgan, a former close adviser to Tony Blair in Downing Street, has taken the dispute over Ofsted's governance and independence to new levels, opening one of the most public splits in the life of the coalition to date.

Critics of the government believe that Gove is growing increasingly angry at criticism of some free schools by Ofsted, and particularly the way they are allowed to employ unqualified teachers. Last year Nick Clegg tore into Gove for allowing unqualified teachers in free schools, accusing him of pursuing an ideological agenda. On Saturday night Gove revealed his plans for new teacher guidelines that will call for a return to traditional classroom discipline. Writing lines and picking up litter are among the "perfect punishments" for bad behaviour, he told the Mail on Sunday.

Morgan, a supporter of the academies programme that is at the heart of government education reform, also hit out at the decision to remove her, saying it was part of a pattern in which the Tories were packing public bodies, including the Arts Council and Charity Commission, with their own supporters.

"I am the latest of a fairly long list of people now who are non-Conservative supporters who are not being reappointed. I think there is absolutely a pattern. It's extremely worrying," she told the BBC.

Downing Street sources said that, while the prime minister backed the decision to remove Morgan, it was the responsibility of Gove. Morgan called for the cabinet secretary, Sir Jeremy Heywood, to investigate: "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. I think there is something going on in the centre that's militating against that.

"I think there is an absolutely determined effort from No 10 that Conservative supporters will be appointed to public bodies. I think that is an issue for the cabinet secretary and the Cabinet Office to look at. It has been a quiet, quiet drip. I'm not talking about Labour people being replaced, I'm talking about non-Conservative supporters being replaced by Conservative supporters."

Gove praised Morgan's "tremendous contribution" to the work of Ofsted. "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," he said.

On Saturday rumours were sweeping Whitehall that Gove intended to appoint Tory donor Theodore Agnew, an insurance magnate who worked with him before the 2010 election, then joined the board of the Department for Education, as the new chair of Ofsted. Last year Agnew, who is a trustee of the rightwing thinktank Policy Exchange, a favourite of Gove's, became chairman of the DfE's academies board.

Asked about Morgan's comments, Conservative party chairman Grant Shapps said: "I don't agree. We have to make sure that we have the right people in place to deliver government policy."

Shadow education secretary Tristram Hunt said: "The secretary of state should have stood up to Downing Street and kept Baroness Morgan in post."

Chris Keates, general secretary of the teachers' union, the NASUWT, said she was not surprised by Morgan's removal and predicted that the education secretary would place more of his supporters in key positions in the runup the general election. She said: " I think we will see more of this. When Michael Gove first came to power he did this removing anyone who had opposed or criticised him and replacing them with Tory supporters. This is just par for the course for this government."

A No 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: Sally Morgan was 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."

A senior Lib Dem source said: "The Lib Dems are not going to stand by and let Michael Gove politicise our schools. Education policy is far more important than rewarding a few Tory cronies. The Lib Dems will not let our children's education be dictated by some Tory donor ideologue."