THE UK has a new Prime Minister, and I’d like to congratulate Theresa May on her appointment.

There may be a world of political difference between us, but on a personal level I’m sure we can develop a good working relationship.

We had a constructive meeting in Edinburgh shortly after she took office.

The main topic of conversation was of course the EU referendum result, and how we can respect the overwhelming Remain vote in Scotland. I was pleased that she said she expressed a willingness to consider any options that the Scottish Government puts forward to secure our relationship with the EU.

But today I want to reflect on something else about that meeting.

Putting politics aside, the image of a female Prime Minister and a female First Minister shaking hands on the steps of Bute House is one which I hope inspires girls everywhere to believe that nothing should be off limits to them.

But let’s be frank - there’s still some way to go on the issue of gender equality.

During a TV interview about Theresa May’s appointment, I was asked how my husband felt about me being in a leadership position!

I don’t remember any of my predecessors being asked that same question about their wives.

Theresa May is of course only the second female Prime Minister in the history of the United Kingdom.

It’s safe to say that people remember the first - Margaret Thatcher - for many reasons, but few could argue she did much to advance gender equality.

I was reminded of this when I saw a photograph recently that showed her sitting in the front row of her Cabinet - one woman flanked by 23 men.

In 11 years, she appointed only one woman to Cabinet. She never acknowledged that ordinary women might need help with childcare or educational opportunities to follow in her footsteps.

I like to think that in the short history of devolution, we’ve done a bit better.

At the outset of the Scottish Parliament in 1999, Scotland’s political parties were all led by men. There was a male First Minister and a male Presiding Officer, and even the Lord Advocate - a position which long predates devolution - had never been a woman.

Fast forward 17 years, and all of those positions have been held at some point by women.

That’s certainly encouraging, but it means very little if those of us who make it into top jobs pull the ladder up behind us - not just in politics, but across society.

When I became First Minister, I immediately appointed a gender-balanced Cabinet - one of only a handful in the world.

And thanks to proactive steps the SNP took to ensure more female candidates standing for Parliament, the percentage of female SNP MSPs elected in 2016 increased from 28% to 43%. Unfortunately that increase was not reflected across all parties.

All of this is important. A Parliament that is truly representative of all of Scotland - across all demographics - is far better equipped to take decisions that truly reflect the diverse needs of our society.

What’s true for Parliament and Government is true for wider society as well.

In the private sector, there has been some - if insufficient - progress among big business. A study last year found that over a quarter of board members on FTSE-100 companies were now women, more than double the amount recorded in 2011.

180 organisations from across Scotland’s private, public and third sectors have now signed up to the SNP Government’s pledge to aim to achieve gender balanced boards by 2020.

More widely, we’re working to address the barriers that prevent women from reaching top jobs.

Like access to affordable childcare, which is our single biggest capital project this term - increasing free provision for pre-school children from 600 to 1140 hours a week by the end of this parliament.

Or addressing the skills gap by introducing measures to encourage young women to take up Modern Apprenticeships in careers such as science, technology and maths.

Women are still more likely to take time out for work for caring responsibilities, so we’ll work with employers to pilot ‘returnships’ in Scotland helping women who have career breaks return to work.

None of these steps will, by themselves, solve complex issues overnight, but only with a continued focus on these issues will we level the playing field.

There’s more we can do, and there’s definitely a lot more Westminster can do.

Many of the decisions taken by the Tories in recent years - such as welfare cuts and state pension age changes - disproportionately affect women.

So as Theresa May gets her feet under the table, I wish her well - there’s no shortage of challenges facing her. There are many issues which we disagree on, but I hope gender equality is one area where we can work together.

Maybe then, the media might worry less about what our husbands think…