Theresa May’s new year video message looked a bit like a royal address: artfully shot in front of a grand Downing Street mantelpiece, a twinkle of seasonal lights relieving the trademark severity. Firmly upholstered in a navy blue jacket, as if taking a brief break from the slog of EU negotiations, May promises a “greige” Brexit, nuanced enough to appeal both to Brexiteers fretting that their victory last June will be unwound by a concatenation of courts, civil servants and parliamentarians – and remain voters too vociferous and numerous to be merely swept aside.

The prime minister's knack is to make contentious issues sound dull enough to lull all but the most energetic dissenters

An outbreak of healing unity after the fissures of 2016 is the implied covenant as the prime minister embarks on a countdown to triggering article 50 by the end of March. Out with the remnants of 2016 goes strident rhetoric about arrogant liberal elites, so feistily deployed at the Conservative conference. “Last year’s words belong to last year’s language,” as TS Eliot might have noted of T May.

Carefully balanced commitments are being made to appease both sides. The prime minister’s default knack is to make contentious issues sound dull enough to lull all but the most energetic dissenters into submission. A couple of senior backbenchers, summoned to pre-Christmas chats about the febrile mood among MPs, described the process to me as “like Kaa in The Jungle Book mesmerising Mowgli”. The charge that May has been evasive or uninformative in her approach to Brexit in the latter half of last year misses the point – that is precisely her modus operandi.

Summoning up the memory of the “fantastic MP Jo Cox” in her address will irk those who believe that the Labour parliamentarian’s murder was in some way related to a divided national mood. But it appeals to a broader feeling that the fractiousness needs to abate in the coming months. As strongly as many feel, an awful lot of voters have had enough of the wrangles and hanker for some kind of certainty about what comes next.

Getting to this point, however, entails a formidably tricky act of political triage, determining the priorities that will shape not only the technical structures of Brexit, but its tone and pace.

It has been fashionable to dismiss her “Brexit means Brexit” mantra as vacuous. But using it sends a simple but necessary message: namely that she will trigger article 50 and deliver an exit from the EU on clear terms in short order. Not such an empty pledge, given the original intention by soft Brexiteers that it would end up meaning something very like remaining.

Delphic pronouncements have already bought her time to square competing interests on her team. So Liam Fox, originally positioned as the most vigorous Brexit warrior in the cabinet, has given ground on the possibility of the UK remaining in an EU-based customs union, while David Davis has suggested that Britain could pay for single-market access. Philip Hammond, despite a Downing Street omerta on phrases such as “transitional arrangements”, has declared that a period of “smooth” Brexit could take up to four years.

Smooth, greige or plain equivocal, these concessions hint at the kind of compact May needs to reach among her cabinet and MPs. She will never overcome the opposition of those who believe that exiting the EU is a heinous act, or satisfy spiritual Faragists, who desire a continent cut off by fog. But she does not need to do either. A Brexit mode that non-combatants think represents a not-bad outcome, and a sense that she has endeavoured to find reasonable compromises, will suffice.

For those who wish to play their part in future acts, this poses challenges. Boris Johnson, the foreign secretary, remains the most outspoken critic of remaining in a customs union – a measure that has come to stand for remaining close to existing EU trade arrangements. That leaves him as the standard-bearer for vigorous Euroscepticism – though boxed in by other cabinet roles. A second Boris offensive on the leadership is a date that could easily slip into the never-never, the latest chapter in the Arthurian legends of Ken Clarke and Michael Heseltine as prospective leaders never able to get the sword out of the stone.

In the more forgiving light of a new year, hatchets are being buried in the Tory tribe. May’s conciliatory tone is intended to encourage more of that. So Michael Gove, an intellectually respected player despite his ousting from the ministerial Premier League, writes on ConservativeHome that “it is critical that we recognise and respect the concerns of the 16 million who did not vote to leave” – a late-breaking emollience. Those who wish to play a role in the Tories’ near future have been given to understand that wherever they stood in the bitter internal wars of 2016, they must sheathe their resentments,

That leaves the other great absentee, George Osborne, with an intriguing choice to make. The former chancellor has been, at least in the eyes of No 10, the most sore loser of the Tory remainers. Yet he is also the character most driven to make a return to front-line politics. In 2017 the accessory required of those wishing to prosper under the May supremacy will be an olive branch, even if the bearers come with gritted teeth.