The prime minister is breaking her holiday in the Italian lakes to visit the French president at his official holiday residence off the Riviera for talks reportedly solicited by the British side. Cabinet ministers meanwhile are fanning out over Europe, with the foreign secretary, Jeremy Hunt – less than a month into the job – stopping over in Paris and Vienna on his way back from China.

Now no one could possibly begrudge Theresa May her week or two of respite after the last fevered month of the parliamentary term, and a side-trip to the south of France hardly counts as deprivation. Indeed, the Macrons incurred the wrath of the French public by asking for a swimming pool to be installed to supplement their private beach. Nor is it uncommon for national leaders to visit each other on holiday. It was routine for Soviet and Russian leaders to hold court beside the Black Sea, and there were summers when, for instance, Silvio Berlusconi seemed to be running something akin to a pan-European timeshare at his Sardinian villa.

The UK’s sudden interest in the EU27, however, suggests something other than recreation. With May’s Chequers proposals apparently failing on both fronts – neither bringing new unity to her government and party nor convincing EU chief negotiator Michel Barnier – the government seems to be adopting a fresh approach that looks suspiciously like divide and rule. Now that the EU institutions are safely en vacances, the idea would seem to be to sound out key national governments individually – and press key national interest buttons – in the hope that they will in turn decide to bend Barnier’s ear.

The rationale can be well understood. May’s pitch to Emmanuel Macron is expected to focus on European security, the gap that leaving could create in that sphere and the mutual advantage to be drawn from the UK’s continued participation in information-sharing. Vienna is equally well chosen for Hunt’s flying visit, given the complexion of the Austrian government and its concerns about borders and migration. Poland, the Baltic states and Italy must surely be among the next destinations on UK ministers’ holiday route.

All of which marks in some ways a welcome change. It is positive to see the UK engaging in some pro-active European diplomacy and going beyond Brussels and the old standby of Berlin. If this amounts to a recognition that Angela Merkel’s power may be ebbing and the EU centre of gravity may be shifting, then that hints at a welcome sense of realism, even if it has come a bit late in the day.

Jeremy Hunt with the Austrian foreign minister, Karin Kneissl. Photograph: Ronald Zak/AP

The deployment of Hunt also suggests that the Foreign Office may be making a comeback in policy regarding the EU. Boris Johnson was kept about as far from European matters as it was possible to be; and the tone has changed. Hunt has come in with a combination of charm offensive and warnings to France and Germany that the danger of the UK “crashing out of the EU” was “increasing by the day”, and that this could be as damaging to the EU – a “tragedy” even – as it would be for the UK.

How much ice will any of this cut with either France, Germany or the EU as a whole, however? If London has any expectation of sowing division, with a view to extracting a better deal – or any deal at all – it could well be disappointed. Over the year and a half since the UK invoked article 50, the EU27 have shown a remarkable cohesion. There may be discord on sharing responsibility for refugees, on Poland’s proposed judicial changes, on free movement, on reform – or not – of the eurozone, and on Macron’s vision for a Europe at once more flexible and more integrated. But on Brexit, it has been hard to detect any cracks.

Forecasts that the Brexit vote could encourage others to follow suit have not been borne out. On the contrary, the effect seemed to be to foster unity – including on military and defence, where the UK had been an obstacle to closer cooperation. The vagaries of the Trump administration in the US further underlined the advantages to the EU27 of belonging to a larger, friendlier and more familiar bloc.

So London may be embarking on a summer of diplomacy – and the new faces of Hunt and Dominic Raab as chief negotiator offer something of a new start. But an autumn of agreement will only follow if the UK finally grasps that it is the one doing the leaving, that the EU’s shared interests remain strong, and that it is the UK, not the EU, that needs a deal.

• Mary Dejevsky is a writer and broadcaster