Michael Gove, the Chancellor of the Duchy of Lancaster, is set to become one of the major winners of tomorrow's government reshuffle. He appears certain to retain control of the Cabinet Office, and to take on a trio of roles. He is in line to oversee COP26, the UN climate change summit being hosted by the UK in November, and efforts to ensure that conference is part of a government programme to reach "net-zero" overall. He is due to have oversight of Britain's future trading relationships with Europe and the rest of the world. And he is highly likely to take charge of improving the efficiency and delivery of public services – a key plank of Dominic Cummings' plan to fix the machinery of government.

Each role is arguably worthy of a cabinet post in itself. Combined, the roles would make Gove one of the most powerful members of Boris Johnson's government. Only Sajid Javid, through his control of the Treasury, is on course to rival Gove for pre-eminence in cabinet. Dominic Raab may officially remain First Secretary of State, and continue to be Johnson's theoretical deputy, but the Foreign Secretary appears to rival Gove in name only.

Gove – the only surviving member of David Cameron's first cabinet from 2010 – is the latest minister to oversee the Cabinet Office: a relatively obscure part of government that is being increasingly treated as the fourth great office of state, alongside the Treasury, Foreign Office and Home Office. Gove has, says a No 10 insider, "taken what could be a backwater department and made it central. He has made himself extremely valuable, through competence."

The Cabinet Office is now rarely a backwater. The department houses the Cabinet Secretary – the UK's most powerful civil servant – and is the building out of which cabinet committees and the cabinet secretariat is run. It advertises itself as "the centre of the UK government" and describes its role as making sure "the government runs effectively."

Gove's predecessors at the Cabinet Office include Francis Maude and Oliver Letwin, who served under Cameron. Letwin described his role as "a political version of a Cabinet Secretary… and a Mr Fix It." Gove's role is more clearly defined. It may also be more wide-ranging. Gove won the support of almost a quarter of Tory MPs in the 2019 leadership election: his presence at the top of government is not only a practical move – he is widely viewed as a capable minister – but a political decision for Johnson, who Gove famously defenestrated in the wake of the 2016 referendum.

That ill-will is long forgotten, or at least irrelevant for now. Gove, who has known Johnson since their days at Oxford University, has the Prime Minister's confidence. Gove also remains close to Dominic Cummings, his former long-time aide at the Department for Education, and now the Prime Minister's senior adviser. Gove gave the best man's speech at Cummings' wedding in 2011. The pair talk regularly in government.

Their working relationship will be essential. In the early years of the Cameron government, Maude and Letwin worked closely with Steve Hilton and others in No 10 to enact the coalition's agenda. "The Cabinet Office has always been an extension of No 10," reflects a cabinet minister, "and its ability to get things done."

Other former high-level ministers – such as Damian Green and David Lidington under Theresa May, and Peter Mandelson under both Blair and Brown – have also worked out of the Cabinet Office in a bid to drive the PM's priorities through government. "The aim was to not have just a coordinating function," Mandelson said in 2018, reflecting on his role for Blair, "but [to] be bigger than that." Attempts to turn the Cabinet Office into the Office of the Prime Minister date back to New Labour. They have always foundered on the opposition of the Treasury. Whether that changes under Johnson will depend on the balance of power he wishes to create.

"At the end of the day," Mandelson added in 2018, the prime minister "designs the layers of personal and political machinery he wants to work through – it’s a reflection of his personality." That machinery will continue to take shape long after the reshuffle.

Gove is unlikely to have direct involvement in one notable aspect of the government's agenda: Johnson's ambition to "level up" the country. "That is," says one government minister, "more a No 10 and Treasury thing." Levelling up is largely an economic programme, and will demand central government funding above all else. Nevertheless, one of Gove's probable missions – improving the delivery of public services – will indirectly impact the project, and could prove crucial to its success.

"If you are," says a No 10 source, "going to more effectively change things which have been elusive in the past – like the economic geography of the country, or tackling division and inequality – then you need government to work better."

Those close to No 10 stress that Johnson's team will not choose between reforming government and their domestic agenda. It is not only possible to do both at once, they argue, but necessary. One likens it to "building a car as you drive it, which underlines how difficult this task is, but you've got to do both." Reforms will, however, be iterative rather than revolutionary.

The third part of Gove's likely role – the delivery of public services – is the least reported. One insider describes it as "an area that's bedevilled by buzzwords, but things like digitalisation and big data are going to change the way in which we get access to the things we need. A lot of thinking is going on about what that means for government. Quite a lot of it defiantly unglamorous."

The Cabinet Office has often been overlooked on Whitehall for lacking the glamour of the buildings on the other side of Downing Street – the Foreign Office and Treasury. But under Gove, what it lacks in grandeur it may make up for in power. It is set to be the engine room of government.

Update (16:03, 13 Feb): Gove has, as outlined, remained in the Cabinet Office. In the wake of Sajid Javid's surprise resignation, Alok Sharma has been appointed minister for COP26. That may not preclude Gove's involvement with COP or with getting the government to "net zero". Zac Goldsmith was tipped for the role Sharma has been given, but with the caveat that Goldsmith would report to Gove.

Update (15:59, 15 Feb): Gove has been handed oversight of the government's constitutional review into the role of the judiciary. This may be in lieu of the COP post, or in addition to overall insight of the "net zero" brief. The overall picture remains clear: Gove is running a widely-powerful Cabinet Office, and handling at least three cabinet-level posts.