Downing Street will on Monday be dragged into the row over the sacking of the former Blair aide Sally Morgan when the cabinet secretary is asked to explain a "pattern of behaviour" that has seen the removal of a series of non-Tory supporters from high-profile public bodies.

As Michael Gove defended the removal of Lady Morgan, chair of Ofsted, as "good corporate practice", shadow cabinet office minister Michael Dugher said he would write to Sir Jeremy Heywood after the sacking of several high-profile figures.

Dugher told the Guardian: "There are questions to answer about what seems to be a pattern of behaviour in Whitehall where non-Conservatives are replaced by Conservatives."

The move by Labour follows the removal of Dame Liz Forgan as chair of the Arts Council, Lady Andrews as chair of English Heritage, and Dame Suzi Leather as chair of the Charities Commission.

There will be further pressure on Gove when Sir David Bell, his former permanent secretary who is now vice chancellor of Reading university, calls on him to recognise the importance of opening up to different voices. Writing for The Conversation, Bell mocks Gove's criticism of the "blob" – his dismissive description of the educational establishment.

"The [row over Ofsted] shows the importance of retaining, and being seen to retain, independent voices near the top - not simply 'yes men'," Bell writes. "There is a far wider group of non-Blobberati voices across the schools sector, higher education, industry and the voluntary sector, who offer an intelligent critique of where we are now."

The row over Morgan's sacking is likely to overshadow the start of the government's "education week". Gove will kick off a week focusing on the government's education reforms by making clear his determination to press ahead with his highly traditional approach when he says he wants to tear down the "Berlin Wall" separating private and state schools.

Gove confirmed he would not renew Morgan's contract as chair of Ofsted when it ends in October.

His decision has prompted an angry response from David Laws, the Liberal Democrat education minister, who instructed aides to say he was "absolutely furious at the blatant attempts by the Tories to politicise Ofsted".

Downing Street hit back at the Lib Dems. A senior source said: "We know what they are doing, trying to differentiate and show relevance. We are just getting on with running the country."

Labour intensified the pressure on Gove, highlighting the wider implications of Morgan's sacking by pointing out that Tories are filling up public bodies.

Andrew Sells, an investment banker, venture capitalist and large Tory donor, was confirmed as chair of the government's nature watchdog, Natural England, last month.

David Prior, the Charterhouse-educated former chief executive of the Conservative party and son of the former Tory cabinet minister Jim Prior, was appointed chair of the Care Quality Commission last year.

Lady Hanham, the former local government minister who was Tory leader of the Royal Borough of Kensington and Chelsea, was appointed interim chair of the health regulator Monitor in January.

One Whitehall veteran said: "There is a battening down of the hatches. The Tories think the election is looking a bit dicey – so they are thinking, 'Let's get our people in.' They seem to think that if they put people in they will keep hold of institutions."

Nick de Bois, secretary of the 1922 Tory backbench committee, said "so what" if the party is packing public bodies with supporters. The MP for Enfield North told Pienaar's Politics on Radio 5 Live: "Look, there's lots of people with good talents out there. I have no problem if a government that's elected with firm views and ideas about what it wants to do – in this case in education – puts people in place with talent that happen to be Conservative supporters."

Labour will say that the removal of Morgan, who was appointed to the Ofsted post by Gove, highlights a pattern of removing non-Tory figures. Dugher told the Guardian: "I will be writing to the cabinet secretary over what seems to be a pattern from Michael Gove's modus operandi at the Department of Education, replacing non-Conservatives with loyal Tories.

"They are using civil service appointments to hire political placemen. There is a danger of impugning the integrity of the whole civil service appointments process with this perception." He will highlight the role played by Laura Wyld, a former Conservative staffer, who was appointed last year to the civil service post of head of the prime minister's appointments unit.

Dugher added: "Michael Gove said that appointments are made on merit. Well, on that basis Gove would have gone months ago."

A Downing Street source said of Dugher's move: "This is a truly desperate attempt by Labour to grab a few headlines. Any serious examination of the facts – including the government's decision to give senior roles to a series of prominent Labour figures like Alan Milburn, John Hutton and Simon Stevens – demolishes their flimsy thesis.

"In contrast, when Labour was in power it systematically packed key public positions with its supporters. Tonight's intervention exposes Labour's breathtaking hypocrisy."

Gove will try to move on from the Morgan row when he launches the government's "education week" today. In a speech to the London Academy of Excellence, the education secretary will say: "Instead of reinforcing the Berlin Wall between state and private, as the current Labour leadership appear to want, we should break it down.

"Our academies and free schools programme is also starting to erode the boundaries between independent and state. Many independent schools are already sponsoring or co-sponsoring state academies – sharing their expertise, spreading their excellence."

Speaking on the Andrew Marr Show on BBC1, Gove made clear that he would like a renewed focus on traditional discipline.

He said: "The one in three teachers who say that they're uncertain in polling about the measures that they can deploy in order to keep order should be reassured by the government that they have a full range – from verbal reprimands through to lines and essays and up to and including community service.

"It is absolutely right to say to students that if they have in some way undermined discipline or contributed to the deterioration of the fabric of a school building, that they should be responsible for clearing up after school lunch clearing up litter or weeding the school playing field.

"People need to understand that there are consequences if they break those rules and that teachers have the power to enforce them."