In a speech in Stirling on Thursday, the prime minister gave some thought to something the UK too often takes for granted: the UK itself.

She acknowledged our union of four nations has come under unprecedented strain as a result of Brexit. And she recognised the threat it faces here in Scotland from a nationalist government that uses all its considerable powers at Holyrood to campaign for independence.

Her response was considered and heartfelt. She explained why the union matters, looking at the principle that lies behind it and the benefits it brings.

Yes, she talked about the economic advantages the union creates for all of us – the currency we share and our integrated internal market. But her arguments went further. As she said, the UK is more than just a marketplace for goods. It is a family of nations and a union of peoples with common values and a long shared history together.

Our union endures because it has the support of the people who have joined forces to make it. At the same time, it respects our different identities. Indeed, it allows for multiple layers of identity. Scottish and British or British and Scottish. Both, either or neither – the union does not make you choose.

“Diversity is part of the deal,” as May put it.

The third key strength she highlighted was this: our union is defined by how we face up to challenges together. We freely pool our resources, whether that has been to fight external threats in wartime or build economic prosperity in times of peace.

Theresa May making a speech in Stirling on 4 July. May spoke of how her successor will make strengthening the union their top priority. Photograph: Andy Buchanan/PA

In short, we achieve far more together than ever we could apart.

The prime minister’s speech was a welcome articulation of what it means to be British. Of why the union matters. I hope it is remembered as a really important moment – the moment, in fact, we determined that protecting our union must be our top priority.

For that to happen, her successor must seize the opportunity before him. That means delivering a Brexit that works for the whole UK, including Remain-voting Scotland. It also means ensuring that, from top to bottom, the UK government is geared towards strengthening the union.

It will require a change.

Up to now our approach to the constitution has focused on the nuts and bolts of devolution. We have dealt with powers and processes and structures; the mechanics of inter-governmental relations.

It is important to get that right, of course, and discussions between the UK, Scottish and Welsh governments continue on a wide range of issues. In the past few days we have agreed a set of principles to underpin our future joint working. We are also making good progress on agreeing new common frameworks to replace some of the EU rules and regulations that apply at present.

Separately, I’ve been working with counterparts in the Scottish government on the complex transfer of welfare powers that we legislated for a few years ago. All of this matters and, on Wednesday, I expect to answer questions on the details from Westminster’s Scottish Affairs Committee.

But fine-tuning devolution will not, on its own, strengthen the union. That is why I warmly welcome the prime minister’s announcement of a review of UK government structures by my former Scotland Office colleague Lord Dunlop.

I am confident Andrew can take a big step towards effecting that important change in mindset. When the UK government thinks constitution, we need to think about strengthening the union, not just delivering devolution.

As the prime minister said, we need creative ideas for demonstrating the value of union across our four nations.

The reason for that is simple. In Nicola Sturgeon, Scotland has a first minister whose only true priority is pursuit of independence. She poses as a defender of devolution while seeking to destroy it. She seizes on the problems of leaving the EU with unseemly glee. But it is easy to see why. A difficult no-deal Brexit would not only damage our economy, it would fuel nationalist claims of a UK that is insensitive to Scotland’s needs.

The new prime minister faces considerable challenges, and the future of the UK is high on the list. But, like Theresa May, I believe there is cause for optimism. With a positive story to tell and a will to demonstrate the value of the union to all parts of the country, her successor can build a stronger UK.