The question I hear most from Conservative and Liberal Democrat MPs is: who will be Labour's next leader? Yet the question that Labour’s activists ask me more than any other is: who will be picked as shadow chancellor? They think, rightly, that the appointment will shape the next leadership’s political positioning in a far more profound way than whoever emerges from the deputy leadership contest.

The next Labour leader – rather like the Prime Minister – faces two constraints in picking the role. The first is political – your ability to pick your preferred shadow chancellor rests on your own internal power and the scale of your mandate – and the second, equally importantly, is about personnel: your chancellor-designate actually needs to be able to do the job, one of the most difficult roles in both government and opposition.

In the dying days of the 2019 Conservative leadership race, when everyone knew that Boris Johnson was certain to win, and the focus turned to the identity of his top team, I asked essentially every Treasury official, past and present – and a host of former ministers and special advisers – who they thought could do well in the job and what qualities they needed.

The exercise produced just eight names out of a parliamentary party of 317: Ken Clarke, Matt Hancock, Greg Clark, Sajid Javid, David Gauke, Liz Truss, Greg Hands and Philip Hammond, the incumbent. Just three of those names appeared on every list and some were flatly singled out as unfit for the role by others. They agreed on the criteria, however: they needed to be able to absorb the detail and information, master the brief, sell the party’s position in the Commons, run the department and set dividing lines in concert with the prime minister.

Although a number of people I spoke to now believe that Rishi Sunak, the chief secretary to the Treasury, could now step up to the role, Clarke, Gauke and Hammond are, of course, out of parliament, so the shortlist is actually smaller despite having a bigger parliamentary party to choose from.

Fortunately for Labour, the job is easier to do in opposition – several of the civil servants I asked thought that, if the Conservatives were to somehow lose the 2019 election, the likes of Neil O’Brien, a former special advisor to George Osborne or Theresa May, who has yet to hold ministerial office, would more than capable of holding the role of shadow chancellor – but it’s still very difficult.

One of the underappreciated bits of good fortune enjoyed by Jeremy Corbyn was that when he came to power, there were in reality just 13 MPs who were politically aligned to him and he was astonishingly lucky that among their number was one politician – John McDonnell – who had the abilities to serve as shadow chancellor. He was also fortunate in that because he didn’t have a parliamentary power base, he didn’t need to use the role to balance his internal coalition. He could just pick the only real candidate for the job.

One of Ed Miliband’s difficulties was that there was no one in the Parliamentary Labour Party who had all of the necessary qualities to be his shadow chancellor. Alistair Darling, Jack Straw, Ed Balls, Yvette Cooper, Liam Byrne, Angela Eagle and Stephen Timms could all plausibly do the job. Byrne was out of contention thanks to his “no money left” letter, Darling and Straw had both headed voluntarily onto the backbenches, and in 2010, because Labour MPs still elected shadow cabinet members, Eagle and Timms were unavailable. Faced with a choice between Cooper and Balls, Miliband chose Alan Johnson, who struggled in the role. He ended up having to pick Ed Balls and never had the political capital to move or replace him even as various holders of the shadow chief secretary role gained the qualifications necessary to hold the role.

In 2015, many of the campaigns briefed who their shadow chancellors would have been in the event of victory. The reality is that, whatever Andy Burnham and Liz Kendall’s personal preferences had been, they would have had to offer the role to Yvette Cooper, unless they had enjoyed a genuinely crushing victory over her. Whatever the campaigns may say, their choices are more constrained than they would like to think.

I’ve been performing a similar task with the role of Labour’s next shadow chancellor, asking officials, former special advisors, ministers and assorted others who they think could do the job. The exercise has again, produced a similarly short list: John McDonnell, Yvette Cooper, Rebecca Long-Bailey, Rachel Reeves, Ed Miliband, Keir Starmer, Anneliese Dodds and Hilary Benn. And again, many on that list drew equally sharp rejections. Just four were ever-presents: McDonnell, Cooper, Miliband and Reeves. There is a great deal of vacant ideological and political real estate between those four – many in Labour would be disgruntled by all of those picks. In any case, one of them, McDonnell, is unavailable, having ruled himself out.

The difficulty of filling it – and the political choices that are cut off just because of the difficulty of the role – is one reason why the question of “who will Labour’s next shadow chancellor be?” is much trickier and more difficult to answer even than the question of who will emerge as its next leader.