There was a moment in last Wednesday’s televised leaders’ debate from Salford when I realised just how powerful a message the SNP’s anti-austerity alternative to the Westminster establishment is – not just to voters in Scotland, but to people from all across the UK.

It was at the half-time interval, when the other protagonists and I were given the chance to step away from our podiums and gather our thoughts during the three-minute advertisement slot.

It was at this point I took the opportunity to come forward and chat with some of the members of the public in the front rows of the studio audience.

And the conversations I had brought it home to me just how persuasive and compelling that anti-austerity message is, as some of the people I spoke to told me that they wished they had the opportunity to vote for SNP candidates in England. It was validation of the approach we have adopted to this election campaign, and personally it buoyed me hugely going into the second half of the debate.

It is natural to be apprehensive ahead of an encounter as high-profile and important as last week’s contest, and I don’t think myself or any of the other leaders would be entirely truthful if we said we had not experienced any nerves. The opening half of the debate had already given me confidence that the SNP’s message was finding its mark, but my interval chat with the audience fired me up for the remainder of the contest. I knew I was speaking not just for many people in Scotland, but for the very many across the rest of the UK who effectively feel disenfranchised by the policy menu offered by the establishment parties at Westminster.

This election is one like no other in modern times, and the power of the Westminster establishment is being challenged as never before. As such, it is no wonder that the polls show those establishment parties are heading for their lowest combined share of the vote in many decades and that, once again, no single party is likely to command an overall majority. Contrary to the opinions expressed by some commentators, this is no bad thing for democracy; rather, it is a great opportunity for change.

Scotland’s experience since 1999 has shown how both coalition and minority governments can work well. The SNP’s experience of the latter from 2007 to 2011 saw us pass legislation on a vote-by-vote basis, and was a stable administration.

As deputy first minister in that government, I learned how to balance sticking to your principles with making the concessions needed to get the work of government done. And I learned how influential smaller parties can be when they have a good idea, when they work hard to keep you to your word, and when they encourage you to be bolder. I also learned that when you have principles you should stick to them, even if you lose the vote, because you will be respected more for that. That system, of regular cooperation and negotiation, led to better solutions in Scotland.

And that is what SNP MPs will bring to Westminster. The Fixed Term Parliaments Act makes minority government possible at Westminster in a way that wasn’t previously practical. A government cannot lose office simply by losing a vote, and instead there must be a specific vote of no confidence. We want to work with a progressive government, not destroy one, and if we have a role to play in a future Westminster parliament that is what we will do.

The SNP’s proposals at this election show we can steer away from the Tory, Labour and Lib Dem cuts consensus and instead invest sensibly while still tackling the deficit – a proposal that has been given independent endorsement by the Institute for Fiscal Studies.

I’d like to address the matter of the leaked UK government memo about my meeting with the French ambassador. This story has already been shown to be 100% untrue – having been comprehensively rejected by both the French ambassador and consul general.

I am therefore writing to the head of the UK civil service, Sir Jeremy Heywood, requesting an urgent inquiry into the circumstances of such a false account being leaked for transparently political motives.

In the meantime, I repeat my challenge to Ed Miliband: if together our parties have the numbers required after 7 May, and regardless of which is the biggest party, will he and Labour join with us in locking David Cameron out of Downing Street?

Nicola Sturgeon is first minister of Scotland