On Saturday, I stood on the steps outside the Senedd, listening to the leader of Plaid Cymru, Rhun ap Iorwerth, take questions from the media. It was one of those rare moments of almost feeling history being made. As one of the other journalists said to me: “I have never seen a political event like this in Wales.”

A crowd of Plaid supporters had gathered to welcome their 43 new MSs. People were giddy with excitement: for the first time since the party was founded just over 100 years ago, it was about to form the next Welsh government. And for the first time in Wales’s history, the country’s highest-ranking political representative would be from a party committed to securing independence – to breaking away from the United Kingdom. Some of the Senedd members were crying. The crowd starting singing the Welsh national anthem, Hen Wlad Fy Nhadau, and were joined by the assembled politicians.

As for Welsh Labour, the section of a party often described as having been “born” in the industrial heartlands of Wales, this was the first time in a century it was not the biggest party here. It was not even second. It was in third place behind Reform UK.

The results in Wales will set Reform up very well for the next general election. Its 34 MSs will each have an £80,000 salary and three to four members of staff, and, in the Senedd, they will get £1.2m in funding for their group staff. These are serious resources that the party will utilise to build a platform for the 2029 election.

That said, to judge Nigel Farage’s party by its own words, it wasn’t a great night. Farage had previously said it was aiming to win a majority in Wales or at the very least be the largest party and form the next government. But it fell well short of this.

With 34 seats (on 29% of the vote), Reform was far behind Plaid’s 43 seats. Perhaps the biggest indication of the party’s disappointment was the fact Farage didn’t show his face in Wales on results day. It was almost impossible to avoid him in England, where Reform has added more than 1,400 councillors to its ranks, but he didn’t come to Wales at all.

There were rumours (subsequently rejected by Reform) that, if the party did well, he was going to turn up in Newport where the count for its Welsh leader, Dan Thomas, was taking place. But Farage was nowhere to be found. It was a similar story at the Caerphilly byelection last year, when he was in the area during the day, but left swiftly as it became clear Reform was going to lose.

It tells you something about his party: it is simply unable to tolerate even the perception of failure. When you don’t have a moral underpinning to what you are trying to do, your entire raison d’etre is winning. That is why so many Tories have defected to Reform, because it is seen as a vehicle for winning power. As soon as you are not winning, what are you for? The result also hurts the party’s claim to be the voice of the people: it’s a line that becomes harder to sustain when more than 70% of voters demonstrably don’t want the party to be their voice.

So, what should we expect from the new Plaid Cymru minority government? If you look at its 100-day plan and manifesto, it will be seeking to immediately begin negotiations with the UK government on a whole range of concessions for Wales. It wants to see control of rail, justice and the crown estate devolved from Westminster (as they are in Scotland). Plus, it wants Wales to get a fair share of rail funding after the Great Welsh train robbery (effectively, a Treasury accounting trick over HS2 that denied Wales billions of pounds). Add to this changes to the Barnett formula, and it’s quite the shopping list.

But what is really interesting about these demands is that they are not particularly radical in Wales: in fact, many were also Welsh Labour policies. In other words, Plaid will be taking to Westminster policies that the former Welsh Labour leader, Eluned Morgan (who lost her seat on Friday), was unable to extract from the UK government.

Will Plaid fare any better? It certainly believes so. Ap Iorwerth has told me what his strategy is. He will be willing to make the negotiations public and “embarrass” the UK government into making concessions; his wager is that a more antagonistic approach will force Westminster to yield.

Keir Starmer (or whoever replaces him) is in a really tricky position. Labour is down to just nine seats in the 96-seat Senedd. The evidence suggests that one of the key reasons people went from Labour to Plaid was because Plaid is perceived as better at standing up for Wales. If a Labour government refuses Plaid’s demands, it will only feed the narrative that it doesn’t care about Wales. If it gives in to Plaid’s demands, it will hand ap Iorwerth a massive win it was unwilling to give to its own Labour colleague, Morgan.

When you stand back and look at the numbers, two things are clear. One is that Plaid’s mandate in Wales is actually bigger than Starmer’s in the UK: Plaid won 35.4% of the vote in the Welsh election, while Starmer’s Labour picked up 33.7% of the general election vote in 2024. The second point is that electoral systems really matter: remember, Starmer’s vote share gave his party a crazy 63% of the seats in Westminster, thanks to first past the post. Under Wales’s more proportional system, Plaid got a much more reasonable – and democratically defensible – 45% of the seats.

In other words, UK Labour can blithely dismiss demands for Wales to have comparable powers to Scotland if it wants – after all, this is what it has been doing since 2024. But it holds its majority on the back of an archaic electoral system, which clearly needs to be put on the scrapheap. The democratic deficit at play here is only going to intensify feelings of resentment against Labour in Wales.

The election in Wales has marked a fundamental change in Welsh politics as we know it. How it plays out remains to be seen, but for the first time in living memory the people of Wales have primarily put their faith in parties that do not have a red rosette. If any lesson is to be taken from our election it is that the only consensus now is that the status quo isn’t working. Change is coming: UK Labour can either help shape it, or be consumed by it.

• Will Hayward is a Guardian columnist. He publishes a regular newsletter on Welsh politics