In the moments before the government unveiled its Defence Investment Plan, the two men who have overseen its progress shared a quiet moment in the House of Commons chamber.

John Healey, who resigned as defence secretary because he was unhappy with the amount of money attached to the plan, and Dan Jarvis, who replaced him, could be seen deep in conversation tucked away behind the Speaker’s chair.

When Jarvis took to the dispatch box, he was keen to boast about the extra £1.5bn he’s secured from the Treasury in the few weeks he’s been in the job.

Some in Westminster have highlighted the “collegiate” relationship between him and the Chancellor Rachel Reeves, a contrast to the briefings after Healey’s resignation that revealed his soured relationship with the Treasury.

The extra cash Jarvis achieved brought the overall funding increase for the armed forces to £15bn, which Healey made clear he still didn’t believe was enough.

Sir Keir Starmer had earlier described the plan as “a platform on which I know my successor will build”.

And faced with Healey’s polite criticism in the chamber, Jarvis admitted that “we need to do more” beyond today’s announcement.

When Healey resigned earlier this month, his allies had claimed that “Treasury trickery” had in effect inflated the money that appeared to be attached to the investment plan.

Buried within that plan today were numbers that are likely to cause Sir Keir’s successor as prime minister a headache.

It contained confirmation from the Treasury that only £10.3bn of the £15bn that’s been committed has actually been identified.

The remaining £4.7bn would have to be found at the next Budget, due in the autumn.

That’s a task likely to fall to Andy Burnham and whoever he picks as his chancellor.

Today’s investment plan also relies on £10.7bn of “defence efficiencies” being found by 2030, with little detail about how that would be achieved.

And there’s an assumption that defence will be a key priority at the next spending review, which potentially means further cuts in other government departments.

That raises a question about the priorities of Burnham if he becomes prime minister next month, as expected.

He’s understood to have held constructive talks with Healey about defence spending, but even some of those close to Burnham admit they know little about his philosophy on the topic.

When he outlined his vision for Downing Street yesterday, there was not much talk of bombs and bullets.

Jarvis told BBC Newsnight that he had discussed the investment plan with Burnham, but it’s understood he couldn’t be briefed on certain security issues and did not sign off the full thing.

The defence secretary would not confirm if Burnham had been told that he would need to find £4.7bn to fund the Defence Investment Plan if he becomes prime minister.

The most awkward moments for Jarvis came not from interventions on the opposition benches, but his own, as almost every Labour MP who stood up said the money currently on offer does not go far enough.

That included senior Labour backbenchers such as the chair of the defence select committee Tan Dhesi and the chair of the treasury select committee Dame Meg Hillier.

One Burnham ally described the funding gaps in today’s plan as “another spending pressure” he will have to face.

Those around Burnham may be relieved that Sir Keir has published this plan before he leaves office.

But it’s clear that the rows around defence spending which the outgoing prime minister had to deal with will still make for one of the trickiest issues in his successor’s in-tray.