As Keir Starmer bid a brief and emotional farewell at that pillory of a lectern, there was a moment for some to ask: what have we done, and why? He’s not a bad man, not a Boris Johnson or Liz Truss rogue prime minister. How decadent, if lack of charisma has become a sacking offence.

But the reason why isn’t written in Westminster. It’s there in councils up and down the country where the hard-right Reform UK troopers swept through last month, from Barnsley to East Sussex. Look north, where Sunderland has 58 Reform councillors to Labour’s five. Look next door at South Tyneside, where Labour was nearly wiped out, left with only one councillor. Many Labour MPs now find themselves all but alone, their local parties hollowed out in an alien sea of Reform. Here’s why it matters beyond the green benches, beyond MPs’ personal careers, out in the very real world where services are (or aren’t) delivered locally.

South Tyneside’s new Reform council is consulting on closing 10 publicly run nurseries, suggesting the private sector can provide the places instead for those hundreds of children. (The leader wouldn’t speak to me about the plan.) Stanley nurseries are what’s left of Sure Start, hubs based in council estates and the most deprived places, not only for daycare but baby clinics, parenting classes, dads’ groups, help and services of all kinds. Joanna Taylor, mother of a toddler in a Stanley nursery, is campaigning fiercely with petitions, marches and protests at the town hall. “Our Stanley staff are much better trained, they take Send children the private sector doesn’t and, anyway, private nurseries have waiting lists until 2028.”

The effect of the Farage surge is why Starmer had to go. He has been incapable of galvanising resistance to Reform, which took the lead in national opinion polls by up to 10 points in under a year after Starmer’s “loveless landslide” victory on just 34% of the vote. In More in Common’s latest approval ratings, Starmer scores minus 45, Kemi Badenoch minus one, with Andy Burnham at plus nine. Defenestrating the Labour leader isn’t a little local fracas in Westminster among MPs overanxious to keep their seats – this is about the very real and absolutely terrifying prospect that Nigel Farage could become the next prime minister. Whatever sympathies many feel for the rotten legacy Starmer inherited, this was no time for Labour’s usual reluctance to evict its leaders. The risk is too great.

What good luck that Labour has the only leading politician with a positive popularity score in these cynical anti-politician times. Don’t underestimate his remarkable win in Makerfield, Brexitland that voted Reform heavily in local elections only a month earlier. Forget the hostile trivia (his eyelashes!), what counts is his ability to persuade voters to abandon Reform. He proves Farage is vulnerable to a bold enough bid from the left: centrism and caution and paralysis under Treasury orthodoxy doesn’t cut it. Burnham does.

No policies? That’s the trope from the hostile media that doesn’t report them. Electoral reform is revolutionary. Devolution of power and money to mayors genuinely takes back control. Rent controls for private-sector tenants, lower energy bills with green levies paid by general taxes, capping bus fares at £2 everywhere, cutting business rates for pubs and small shops will be noticed. Nationalising water, starting with Thames Water, and his long-term intent to take back the National Grid to stop profits leaking from vital services. Expect a closer and braver embrace of the EU, chasing that missing 6% to 8% of GDP. Expect a colder, more principled, riposte to Donald Trump and Benjamin Netanyahu. All these, done quickly, can change the national mood.

In the end, getting and spending is what defines a government. We await his choice of chancellor. Will he be deterred from Ed Miliband by hurricane-force attacks from the right and its press? Burnham and Miliband’s economic policy is emerging from outriders and advisers reflecting the many ways to raise money without breaking manifesto pledges. War bonds with reduced inheritance tax would attract investors in defence. Equalising rates for income and capital gains tax is fair and lucrative, closing private equity’s loophole. Jim O’Neill, the Burnham adviser and former treasury minister, ex-Northern Powerhouse chair and ex-Goldman Sachs chief economist, tells the FT the new PM could raise far more borrowing if it were used for much-needed productive capital investment.

Burnham’s mettle will be tested, that tightrope walk between bravery and peril. But courage has to be his hallmark. Some say a hand-to-hand contest would have tested his credentials: wiser heads point to how these rivalries exaggerate differences, obliging candidates to make spur of the moment membership-pleasing promises, later broken or regretted. He is more experienced in Treasury, cabinet and leadership than most new prime ministers, better trained to resist frighteners from the business or Treasury world obstructing his natural instinct for radicalism. Choosing Ed Miliband would signal that strength, appointing the serious economist to set out a Burnham government’s intentions with clarity: it would reassure Labour MPs that there is balance at the top, with Shabana Mahmood at the Home Office and James Purnell as chief of staff. He will step through that black front door to a near impossible job: bad stuff happens all the time, but things can get better.

Where’s the celebration, then? Traditional Labour miserabilists are getting their disillusion in early: he’ll fail, the task is undoable. True, his rating will drop fast. Attacks will be never ending, whatever he does. “The same old s**t, only this time with a Stone Roses soundtrack,” says the Sun already. Political chameleon, lightweight, says the enemy. He’ll prove them wrong if he steers his own course with that difficult blend of optimism and realism, of hope, risk and wisdom. But vanquishing Reform is his prime duty.

• Polly Toynbee is a Guardian columnist