It’s been the refrain of the week. Why can’t the country hold on to a prime minister – and how can it be that Larry, the Downing Street cat, has managed to outlast six of them? Have we become ungovernable? Is it because one government after another has failed to halt the slide in living standards – or have online attention spans eroded our patience for change?

But Westminster isn’t the only dramatic platform casting for a new lead at the moment. Amid the political chaos this week, I was struck by a social media comment that this is the first time the UK has found itself looking for a new PM, a new James Bond and a new lead for Doctor Who, all at the same time.

Bond and the Doctor are, after all, some of the most enduring characters in Britain’s postwar national story. So what might it mean that nobody knows who’s running the country, driving the Aston Martin, or piloting the 1960s police box? It seems Britain can no longer agree on who its protagonists are supposed to be.

Start with Bond, whose character was fixed for decades. He was charming and effortlessly competent, irresistible to women and immune to consequence, a cold-war fantasy of continuing white, upper-crust British relevance in a post-colonial world.

That gravity-defying certainty held more or less steady until Daniel Craig’s Bond started softening around the edges – he cried, fell in love, and got into the shower in his tuxedo to comfort a woman. By 2021, Craig’s final outing had turned into a referendum on Bond’s character and place in contemporary society. The script for No Time to Die was revised by Phoebe Waller-Bridge for the #MeToo era, and the 007 codename was briefly handed to a Black woman. “If James Bond has gone woke,” the Telegraph thundered, “he might as well be cancelled.”

Since then, creative control has passed from the Broccoli family – Bond’s custodians since 1961 – to Amazon MGM, and the casting debate has become a permanent feature of British public life. Should Bond be younger, Black, less of a cartoon relic? But Idris Elba, long rumoured for the role, has now ruled himself out, saying some audiences wouldn’t accept a Black 007. Five years on, we still can’t settle on a successor to Craig.

Where Bond is a fantasy of British power, the Doctor has always represented the nation’s eccentricity, insatiable curiosity and ingenuity. Yet that role, too, has become burdened by questions that have little to do with acting ability. Jodie Whittaker’s casting as the first woman in the role split fans in 2017; Ncuti Gatwa, as the first Black Doctor, was the target of overt racism in 2023.

Meanwhile, the wider orchestration of the show has been in flux. A Disney+ partnership timed for its 60th anniversary failed to restore ratings, and Gatwa left after just two seasons. Now the BBC has put the Doctor’s future out to competitive tender, and the outgoing showrunner, Russell T Davies, confirmed that no actor has been approached to play the next Doctor. Ironically, a show built around regeneration is now part of a national argument about how much change people are prepared to accept.

You could say Westminster has the same problem. Part of the reason we’ll shortly be on to our seventh prime minister in a decade is that the stories politicians once plugged themselves into – postwar consensus, Thatcherism, New Labour, even Brexit – have either fractured or run out of road. There is no longer a settled idea of what Britain is, where it is heading – or even what alternatives politics should be offering.

In its place are competing visions of the country: a diverse, outward-looking nation at peace with change, or a place of cultural and demographic decline, unmoored from its traditional identity. And no one with political weight has succeeded in bridging that yawning gap.

In 1941, George Orwell wrote that nations are held together not just by institutions but by the stories they tell about themselves. In The Lion and the Unicorn, he argued that England was bound together by a patchwork of myths, symbols and shared assumptions. The arguments over Bond, the Doctor and the turnover at No 10 revolve around a similar question: who gets to stand at the centre of the national story, and what script are we asking them to perform?

Reddit users have suggested that perhaps one person should fill all three roles. I reckon Peter Capaldi is a pretty strong candidate – but only if he behaves like Malcolm Tucker. Or here’s a fun game to play at home: why not rotate them around? Perhaps Craig as PM, Whittaker as Bond and Starmer as the Doctor? Starmer couldn’t solve our national identity problems in office, but hey, maybe a time machine could give him a fighting chance.

• Nadia Khomami is arts and culture correspondent at the Guardian