Sir Keir Starmer is lucky with his timing. After spending his first full week in office at a Nato summit – meeting far more world leaders in one go than would normally be possible – the Prime Minister this week had another chance to strike a statesman’s pose, hosting the European Political Community at Blenheim Palace.

The event for more than 40 European leaders was organised by Rishi Sunak – but he was gone by the time it took place on Thursday. Instead it was Sir Keir who reaped the diplomatic and political benefits of a sunny away day in grand surroundings.

By hosting the leaders of Ireland, France and Ukraine for separate one-on-one meetings, the Prime Minister managed to present himself as the new kid on the geopolitical block. But back in Westminster, his team has been careful not to take their eyes off the domestic political prize.

Despite holding a huge majority in the House of Commons, Labour insiders acknowledge that the party’s position is weaker than that of previous big election winners.

Labour won less than 34 per cent of the national vote in the general election, barely better than Jeremy Corbyn in 2019. “Our majority is very soft,” one insider told i. “It’s built on shifting sands in most places.” Large numbers of MPs are sitting on majorities of just a few thousand votes in their own constituencies: even as it won hundreds of extra seats, Labour’s lead in many of the places where it had previously won was dramatically reduced with Reform UK, the Greens and independent candidates benefiting instead.

“We need to do better than 34 per cent next time,” an MP warned. Inside 10 Downing Street, a team led by Morgan McSweeney – the Starmer confidant who led the election campaign – is already at work on ways to shore up support and build towards the next election in 2028 or 2029.

A source said: “We are trying to do the work that the Tories didn’t do – building a voter coalition.” Labour strategists have been struck by the failure of the Conservatives after 2019 to decide which voter group they valued more between the social conservative but more statist “red wall” and the socially and economically liberal “blue wall” – with the result they lost both this time around.

One new Labour MP told i that they were already preparing to campaign for the local elections in May despite sitting on an 8,000 majority – saying: “My team were knocking on doors they’d never campaigned in before. We were walking up driveways with Ferraris sitting outside the house. It was mad. And we had a good reception from people. I’m now getting my team ready to start campaigning for the county council elections in the next couple of weeks. It’s the difference between whether I’m here for five years or the next 20.”

At Westminster parties since the election, newly arrived MPs can be seen openly lobbying Cabinet ministers over their pet topics – and demanding assurances that they will be able to show their voters tangible change by the time they are up for re-election.

One debate within the party is whether the idea of targeting so-called “hero voters” – people who had previously backed Labour but switched to the Conservatives in 2019, often after voting Leave in the Brexit referendum – will remain effective. “The hero voters idea was the right one, but we probably did go a bit too broad,” admitted one strategist.

For some MPs, winning back left-wing voters who have abandoned Labour over its stance on the war in Gaza will be a priority. Foreign Secretary David Lammy announced in Parliament on Friday – the earliest he could plausibly have done – that the Government will restore funding to the UN agency which helps Palestinian refugees, after it was stopped following allegations that some of the body’s staff helped Hamas carry out the 7 October attacks.

Most insiders say they are optimistic that the heat will have gone out of the debate on the Middle East by the time of the next election, making the issue less divisive. But as one source put it: “If we can’t win those voters back, it becomes all the more important to attract more Tory voters.”

Ministers are intent on keeping up a frenetic pace of activity, including during the traditionally quieter summer months. In the last week of July, Rachel Reeves is expected to publish an “audit” of Government spending which she will use to argue that Labour may be forced to make unpalatable decisions around tax and spending cuts.

Angela Rayner is drawing up the next steps on her proposed planning reforms – including firing the starting gun on a new generation of “new towns”. It is understood that an announcement on how the process to identify the sites will unfold could come as soon as August, rather than waiting until Parliament returns from its summer recess in September.

Meanwhile, as well as keeping voters onside Sir Keir will have to contend with his own MPs. While the era of infighting on the Government benches is thoroughly ended for now, there are early signs it will not always be straightforward to keep 411 colleagues onside.

“The problem for No 10 is that there are 400 of us, and only 130 jobs in Government,” one backbencher remarked. “Half of us won’t even get a select committee!” As of this week, the list of parliamentary private secretaries – the ministerial aides who work unpaid as a liaison between Whitehall departments and backbench MPs – has been finalised, meaning that hundreds of Labour MPs know they will need to wait at least a year before they get a foot on the first rung of the career ladder.

Sir Keir handed PPS jobs to a number of new MPs, including Torsten Bell, the respected former head of the Resolution Foundation, who will play a key role as aide to the Cabinet Office enforcer Pat McFadden – and Liam Conlon, son of No 10 chief of staff Sue Gray, who has joined the Department for Transport.

Others will try their luck on select committees, with Labour veterans passed over for Government jobs fighting it out to chair the most high-profile of them. Meg Hillier is favourite to chair the Treasury committee while Emily Thornberry – the only member of the shadow Cabinet to be rejected from the new Cabinet – is said to be keen on the foreign affairs committee, having served as shadow Foreign Secretary under Jeremy Corbyn.

On the other side of the aisle, despondent Conservatives are preparing for a far more vicious round of infighting as they select their new leader. One insider told i: “We’re already in a cold war and no one has declared their campaign yet, just imagine how much worse it’s going to get when the leadership election actually starts.”

Mr Sunak, at least, appears in good spirits – despite uncertainty over how long he will have to serve as Leader of the Opposition, a job he is believed to find intensely uncomfortable. “He seems far too cheerful for someone who has just got most of the MPs sacked,” an unsympathetic Tory said.

The former Prime Minister has gone out of his way to behave graciously to his successor, and the pair enjoyed a warm and lengthy chat in Parliament after the King’s Speech on Wednesday. But he could be forgiven for reflecting that now it is Sir Keir who has all the luck.