As Boris Johnson’s whistle-stop tour of the United Kingdom takes him to Northern Ireland, there are doubtless going to be several serious items on his agenda.

First, of course, there will be the need to advocate for his policy on the backstop. Then there is the obligatory effort to “revive power-sharing”.

But before all that there was a sit-down dinner with Arlene Foster and the Democratic Unionists, and when it comes to the fate of the Government this might prove as important as either of the other two.

The Sun reports that the Prime Minister met not only with the DUP leader but also with Nigel Dodds, the leader of its Westminster group, and Sir Jeffrey Donaldson, its chief whip. On the agenda was not just Brexit and Stormont but, according to Foster, “how to strengthen the bonds between Northern Ireland and the rest of the country”.

Grubby practicalities about the Conservative/DUP confidence and supply agreement, on the other hand, were apparently not discussed… at least last night. But this morning’s Belfast press report that the DUP leader has “refused to rule out” asking for more money in exchange for renewing the parties’ alliance in the Commons.

Even if the two sides hadn’t fallen out over the backstop as Theresa May tried to ram her Withdrawal Agreement through Parliament, such a bid was almost inevitable right from the start. As we noted previously, it was almost built into the structure of an agreement whose terms were expected to run until 2022 but whose price was fully paid out by 2019.

With Johnson unabashedly prepared to splash the cash in his efforts to bolster the Union – just this week he has announced over £300 million of new investment in UK ‘growth funds’ – it seems likely that the DUP will get their extra money for roads, broadband infrastructure, and other investment. Plus with the new, post-Karen Bradley order in place at the Northern Irish Office they may even get one of their biggest asks, direct rule of the Province from London, if devolution fails to get back off the ground.

But with the odds shortening on an imminent general election, and their stated ambition of “strengthening the bonds between Northern Ireland and the rest of the country”, DUP strategists ought to give serious thought to a simple question: how do they best lock-in their influence for the long term?

The 2017 election delivered a result in a relatively narrow margin which allows the Tories to operate a majority with DUP support. It would only take a small shift in Conservative fortunes, in either direction, to move the parliamentary arithmetic out of this window.

Such an outcome would dramatically curtail the Unionists’ influence over the Government. Unlike the Scottish Conservatives, who for all the devocrat fantasies of blocs and breakaways remain an integrated part of the broader Conservative and Unionist family, the DUP have no permanent seat at the table. Their MPs didn’t get a vote in the recent leadership contest, and may not retain their back channels to the Government once parliamentary circumstances change.

Moreover, in 2017 the DUP are rumoured to have ducked a once-in-a-generation opportunity to normalise Ulster voices in British politics by declining an offer of a full-blown coalition, which would have allowed its MPs to serve in ministerial posts.

When the two parties sit down to renew their working relationship, both ought to recognise that any effort to better integrate Northern Ireland with the rest of the country must start by ending the internal exile of its unionist politicians from UK politics. They ought then to seriously explore the possibility of establishing a partnership which can endure beyond the exigencies of  hung parliament.

MPs may have dealt such efforts a helping hand by forcing the Government to extend British norms regarding same-sex marriage and abortion to the Province. DUP intransigence on such issues was a crucial factor in ‘toxifying’ the party in the eyes of mainland observers, and their neutralisation could remove a major obstacle.

Likewise, recent speculation about a part-breakaway by the Scottish Conservatives could furnish a model through which Unionists could part-integrate their Northern Irish fellows, such as creating a Canada-style integrated party or Australia-style permanent coalition for Westminster elections whilst retaining a separate organisation for devolved matters.

All of this might come to nothing. But it ought at least to be explored. The political isolation of Northern Irish unionism has done much to weaken the bonds of the Union. Foster, Dodds, and Donaldson would be doing unionism a grave disservice if they allowed its Westminster representatives to retreat back to the ‘Others’ benches for another forty years.