Credibility is one of those indispensable political qualities that barely rates a mention when it is there. Yet when it is missing, nothing else matters as much. For many voters, Theresa May is established both as a credible leader, and a credible figure of the centre-right. That gives her great scope to launch raids on the centre ground, as she did today with a plan to cap energy prices, which she can claim as evidence of her desire to lead a united country. It may be a reflection of how much more important the division over Europe has become in mainstream politics than the traditional right/left divide. It may signal a more permanent realignment. It is significant that some commentators on the right are already speculating that Mrs May looks set to be the most leftwing Conservative leader for 40 years, with the most rightwing parliamentary party. But what matters in this election campaign is that with her right flank secured she can advance deep into Labour territory, and it can be taken as read that her proposal on energy prices is only a harbinger of the pattern of the next four weeks.

It was also a painful contrast with the Labour leader Jeremy Corbyn, who seemed not even to have persuaded party supporters who had gathered in Manchester for the official campaign launch that he is a convincing prime-minister-in-waiting. An applause line about “when Labour wins” was greeted in silence, and although most of his speech was enthusiastically welcomed, it was, like his hope for a Bernie Sanders’ endorsement, also narrowly directed at energising the party base. It did not sound like the sort of speech that would persuade the people of Hartlepool or Erdington, two Labour-held constituencies where Guardian reporters are embedded for the campaign, to look again at the party some are reluctantly deserting after a lifetime of support. That may not be fair, but politics is often unfair.

Mrs May is clearly prepared to see more intervention in the economy than the Thatcherites in her party. Her proposed energy price cap is not an exact replica of Ed Miliband’s plan, but not many will notice the subtle distinctions around flexibility and the powers of the regulator. Yet when Mr Miliband proposed it the rightwing media denounced it as Marxist and Michael Fallon, the man who is now Mrs May’s defence secretary (and so, presumably, signed up to the policy) declared it actually dangerous. It is rumoured that there was some unease in cabinet; the business secretary Greg Clarke only put up the weakest defence of it in morning interviews. The reason Mrs May persists is because the energy cap signals to Labour voters that the Conservative party could be a home for them.

In rhetorical terms Mr Corbyn red-blooded attacks on “greedy bankers”, “tax cheats” and “the rip-off bosses” are unlikely to win over Tory-leaning voters. Compare this strategy with what Andy Burnham achieved in winning the first Greater Manchester metro mayor contest, considered the most successful Labour result in last week’s elections. In fact he didn’t just win, he triumphed in an exceptional result that put him on 63.4% of first preference votes. His success extended well beyond the predictable Labour heartland of metropolitan Manchester. He won more than half the votes in every borough, and a majority even in wards that make up Tory-held Westminster seats. Few thought Mr Burnham’s campaign flawless. After years of Labour-controlled town halls, the contrast between richest and poorest in the area is almost as stark as it is in London, and on the day the turnout was less than 30%. Yet the former Labour health secretary, a distant second to Mr Corbyn in the final leadership ballot in 2015, found a way to mobilise a victorious coalition around a progressive platform.

Labour’s manifesto is yet to come, but the policies already published do not yet add up to a very coherent platform. Radical ideas on infrastructure investment sit alongside weaker proposals on personal tax. There is a welcome renewal of the last Labour government’s strong commitment on childhood obesity, with a proposal for a ban on pre-watershed fast food TV advertising, but less clarity on, say, policing. Yet in the end, history has an ineradicable lesson: general elections are not won just on manifestos or pledge cards, but also on the believability of the person who is the party candidate for prime minister. Barely a month from polling day, it seems there is no platform Labour could adopt that would address the doubt in many voters’ minds about Mr Corbyn’s credibility as a potential prime minister.