With Westminster in chaos, it has fallen to the governor of the Bank of England to calm markets, households and businesses in the wake of the Brexit vote.

Mark Carney did not mince his words in his latest intervention. The central bank would do what it could and he hinted at a rate cut as soon as this month. But it could only do so much.

So on the day that Tory party heavyweights indulged in Shakespearean amateur dramatics and the Labour party leader, Jeremy Corbyn, embroiled himself in fresh controversy over Israel, over in Threadneedle Street, Carney had a message for the toddlers. It was time for “ruthless truth telling”, he said. “And one uncomfortable truth is that there are limits to what the Bank of England can do.”

In other words, it was time for politicians to get out of their post-referendum tailspin and start plotting a path for our economic future.

At this point, trying to second-guess who will be chancellor and charged with coming up with such plans is a mug’s game. Whether George Osborne remains at the Treasury or someone else takes over, there are immediate priorities to address, and some far deeper issues, too.

So where to start?

It’s a statement of the blindingly obvious, but a clear priority for any chancellor must be seeking to avoid recession. It is not a foregone conclusion that the Brexit vote will shrink the UK economy. Some experts say recession could be narrowly avoided. Others say it is imminent.

Where the chancellor comes in is by shoring up confidence that the UK can weather this storm. If confidence falls, the risk is people delay spending, businesses defer investments and they freeze hiring. All that drags on the economy and recession ensues.

There have been reassuring words and moves by Osborne. In effect, he scrapped his own target to return the public finances to a surplus by 2020. He also assured investors of “robust contingency plans” and quickly rebuffed any suggestion that this could be a rerun of the crisis triggered by the collapse of Lehman Brothers investment bank.

All helpful, but businesses and households will want more clarity on what comes next. They have a long list of questions, including: when will there be a general election? Who will be the next prime minister? What kind of tax and spending policies are to come? When will negotiations with the EU start? How will they end?

With so many uncertainties, it’s no surprise that business leaders are calling for government to put aside party politics. “Lead now,” was the message from Carolyn Fairbairn, director general of the business lobby group the CBI. She worries that what certainty we do have is insufficient to get money flowing around the economy.

She said: “We do have a timetable for a new prime minister. Though this may feel fast in politics, in these circumstances, it’s painfully glacial. The markets and business decisions won’t wait eight weeks.”

That is not to say everything should be expedited. Unprecedented negotiations lie ahead on leaving the EU and forming new trading relationships, and the government must strike a balance between speed and securing a good deal.

Then there are the longer-term priorities. The economy was already slowing before the referendum. Growth slipped to 0.4% in the opening three months of this year, down from 0.7% in the previous quarter.

Such GDP figures get the attention of the media, markets and ministers. But those headline numbers tell us little about people’s economic wellbeing and even less about inequality.

Economists can argue whether inequality is good or bad for growth. But after the referendum, we can pretty much say with certainty that inequality is bad for your career if you are a UK political leader hoping to win a referendum on staying in the EU.

Income inequality and a disproportionate squeeze on living standards for lower- and middle-income households long pre-date the referendum.

As such, when new leaders are in place they will have to make a fresh assessment of austerity. Osborne’s abandonment of his surplus goal is a wise first step but comes after years of cuts have chipped away at vital services, at safety nets and at support for those who want to work or study but struggle to afford it.

The new leaders will have to address the UK’s woeful lack of housing supply, which has helped drive up property prices and rental costs and created a divide between young and old.

The referendum also underscored regional divides in the UK. So while prosperous London largely went for the status quo, most voting areas across the north-east of England sided with the leave camp. A student nurse from Newcastle said to me after the vote: “I asked my dad what to do and he said: ‘Things aren’t good, so go for the change option.’”

Now more than ever, the chancellor needs to ensure his northern powerhouse plan delivers better jobs, incomes and prospects across the region – and not just in its biggest cities.

Tied to this urgent need to improve living standards is the challenge of turning around the UK’s woeful productivity performance. Record numbers of people are in work but the output for each hour worked is barely rising. We can talk about gains being fairly shared out or not, but until productivity improves, there are limited gains to share out.

Getting productivity going again will require more investment in innovation and our universities. It means more help for businesses that want to update their production lines, overhaul their IT systems or retrain their staff.

Productivity will only improve if the UK addresses its skills shortages with sensible immigration policies and with better training. In an age of economic insecurity, training is key if the march of the robots is not to further exacerbate inequality. Similarly, the UK must get serious about moving to an apprenticeship system that has parity of esteem.

Finally, on this long but by no means exhaustive list of tasks, the government must rebalance the economy away from over-reliance on debt-fuelled consumer spending. Export targets look fanciful, manufacturing has yet to fully recover from the last crisis and consumer borrowing is shooting up.

With a to-do list like that, it’s little wonder there are vacancies at the top. The challenges are great and many but, as Carney said, they “can’t be wished away”. And in case that message was not clear enough for politicians, he cited the former US Treasury secretary Tim Geithner’s famous words during the global financial crisis: “Plan beats no plan.”