When the German chancellor was asked this week why she would not railroad Italy and the so-called Visegrád group of countries – Poland, the Czech Republic, Slovakia, Hungary – into accepting the former Dutch foreign minister Frans Timmermans, a critic of populist governments, as European commission president, Angela Merkel’s answer was telling.

“The Brexit is looming on the horizon,” Merkel said in reference to the need to avoid tensions when appointing the next head of the commission. “Other important issues are on the table. I think we need to treat each other with care.”

For all the unity it has shown so far in its negotiations with the UK, the EU is straining to keep its many different constituencies onside across a range of other issues. The next five-year term offers more of the same.

The divergence in values that threatens to cripple the bloc was neatly highlighted at a summit this month when Poland, Hungary and the Czech Republic refused to sign up to a communique that committed to a climate-neutral EU by 2050 – a target that was already seen as too wishy-washy by green lobby groups, given the gravity of the climate emergency.

The UN secretary general, António Guterres, wants to put the world on a path to limiting global warming to 1.5C at a September summit. He had written to Donald Tusk, the outgoing European council president, asking the EU to show leadership on the world stage – and it could not.

The three naysayers are seeking extra recompense for making green changes to their economies in the upcoming seven-year budget known as the multiannual financial framework (MFF), but they will face stern challenge from members, such as the Netherlands, which are firmly opposed to the EU being a “transfer union”.

Indeed the negotiations over the MFF, optimistically scheduled to have finished in May, are predictably proving to be a major headache, leading the EU budget commissioner, Günther Oettinger, to recently warn: “It’s not really five minutes to midnight, it’s almost five past midnight already.”

The package asks net recipients such as France and Germany to pay more as a trade-off for less being handed over in cohesion funds to the central and eastern European states, and more being invested in scientific research and development. But failure to find agreement by the end of October could lead to the EU being unable to fund the next round of Horizon Europe research and development programmes.

The difficulties in the talks are understandable. The divergence in values is matched by an economic divergence from east to west and north to south that the EU has failed to bridge, despite the almost existential threat it posed during the eurozone crisis, when economies unable to borrow on the market had to come cap in hand to Berlin, only to be put on a humiliating diet of cuts as the price for help.

The French president, Emmanuel Macron, has championed a eurozone budget, to allow the EU to act as a sovereign nation in times of trouble, but there has only yet been agreement on a tiny symbolic pot. No wonder, then, that the populist Italian government has raged at Brussels meddling in its tax and spend plans, which it says is necessary to boost its struggling economy.

But as the new leaders in Brussels – Ursula von der Leyen and Christine Lagarde as the first female presidents of the European commission and European Central Bank respectively, and Charles Michel as European council president – move into their offices this autumn, it will be Brexit that will be sucking up their time and energy.

It is certain that the next British prime minister, likely to be Boris Johnson, will not secure the increasingly outlandish potential concessions being touted by the two candidates in the Tory leadership race.

The battle might then be to deal with the economic costs of a no-deal Brexit and a toxic relationship with London at a time when Donald Trump’s White House piles on the pressure through tariffs on trade and China doubles down in its investments in Africa, leaving the EU trailing behind in emerging markets there. Merkel’s commitment to avoiding a row over personnel suddenly becomes more understandable.