When Adam Price was first elected as Plaid Cymru’s MP for Carmarthen East and Dinefwr in 2001, he made his name as one of the toughest critics of Tony Blair in the House of Commons. In 2002, he accused the then prime minister of undue proximity to the steel magnate and Labour donor Lakshmi Mittal, and in 2004 he led unsuccessful attempts to have Blair impeached over his handling of the Iraq War.

So there is more than a touch of irony in acknowledging that when I recently met Price – now Cymru’s leader and the Welsh Assembly member for the equivalent seat of Carmarthen East and Dinefwr – he immediately reminded me of the man he once attempted to put on trial.

The similarity is partly physical – open shirt collar, piercing blue eyes and easy charisma – and partly political. The 50-year-old speaks of the need for Wales to be open and internationalist, is relaxed about business and enterprise, and hopes to take his party from opposition to government. Price has recruited Angus Robertson, formerly the SNP’s deputy leader, to review Plaid’s strategies and practices. So far, so Tony.

But the scale of the challenge is bigger than what Blair faced when he became Labour leader in 1994. Plaid Cymru’s major opponent, Labour, has won every general election in the country since the dawn of universal suffrage and is also the dominant party in local government.

Plaid Cymru, by contrast, is well-liked but has struggled to turn that affection into electoral success. Roger Awan-Scully, professor of politics at Cardiff University, likens the party to BBC Radio 3: voters are glad that it is there, but are not necessarily inclined to tune into it themselves.

The Welsh Labour Party has established itself as a force for what one MP describes as “small-n nationalism”, rather than allowing itself to be portrayed as an adjunct to the Labour Party in England. “Welsh Labour – the phrase trips off even my tongue,” Price sighs when we meet in Coffi Co, a small café on Cardiff Bay.

Although Plaid Cymru has been in office as a junior partner in the Welsh government – Welsh Labour is in coalition with the Liberal Democrats – it has never been in a position to remove Labour from power. Until now. The next Welsh Assembly elections are due in 2021, but if they were held today, polls suggest that a government without Labour AMs (Assembly Members) could command a majority. (Labour has 29 of the 60 seats; the Conservatives have 12, and Plaid ten.)

Plaid Cymru is keen to believe these polls, as parties are when the news is good. But, privately, both Labour and the Conservatives think the surge in support is real. “I can see it on my doorstep,” one Tory MP told me. “Plaid Cymru are on the up.”

Insiders partly attribute this to the change in Plaid’s leadership: Price defeated his predecessor Leanne Wood in a contest in September 2018. He had stepped down from Westminster in 2010 and re-entered politics six years later, spending the intervening time studying for a masters at Harvard, founding a software firm and presenting a documentary about the miners’ strike for the Welsh channel S4C.

The other half of the equation is the change in leadership at Welsh Labour, where Carwyn Jones stepped down as first minister and party leader in December.

For most of his leadership, Jones was the most popular politician in the country. One Welsh Conservative MP once compared Carwyn Jones to David Cameron: neither was a particularly commanding chief executive, but on the campaign trail, they spoke to a particular sense of how Wales and England saw themselves. That Jones was a native and fluent Welsh speaker helped to blunt Plaid Cymru’s distinctiveness. Shortly after the 2015 general election, I asked Jones what he thought Scottish Labour had got wrong. His answer was simple: “I would never let another party take my flag.”

Mark Drakeford, his replacement, is also a Welsh speaker but not a fluent one. His CV includes time as a special adviser to former first minister Rhodri Morgan, and several cabinet posts under Carwyn Jones. He is undoubtedly experienced; the question is whether he is inspiring. One Welsh Labour politician told me that Drakeford “has the ingredients to be a great first minister, but I’m not sure he has the ingredients to be a great candidate for first minister”.

Both Morgan and Jones pursued a strategy of “clear red water”, positioning themselves as more economically left wing than the Westminster party. “Kinda dressing themselves in the clothes of socialism with a Welsh stripe, basically parking their tanks on our lawn: a fantastic political stratagem,” is how Price describes it.

But the rise of Jeremy Corbyn has changed this calculation. Drakeford has described Corbyn’s leadership as an “opportunity not to need a strategy of that sort”. The truth is that as the national Labour party has moved left, it is harder for the Welsh brand to retain its distinctiveness.

“If you can’t define yourself against London, and the strategy of complaining about the cuts is running out of road, what are you left with?” one of Drakeford’s colleagues told me. “Just saying ‘We’re Welsh!’ So? Everyone is Welsh.”

Adam Price wants to make Plaid Cymru the obvious and only candidate to change how politics is done in Wales: to disrupt what he calls “the oasis of stasis”. Can he do it? His opponents certainly fear that he can. “When the Assembly was created,” one Conservative MP tells me, “the answer to the question ‘Who is the most impressive politician in Wales?’ was, obviously, Rhodri Morgan. And then it was, obviously, Carwyn Jones. And now I think the answer is not so obvious.”