If Labour wins the next election, then the title of most important civil servant will belong to a man who retired from the civil service in 2015: Bob Kerslake. The crossbench life peer’s claim to influence lies in his historic relationship with John McDonnell. In the 1980s, when McDonnell was Ken Livingstone’s head of finance, Kerslake was an official in the Greater London Council. Shortly after Corbyn’s election as Labour leader, the two men met and Kerslake agreed to make recommendations on how the Labour leader’s office should run.

The biggest impact came from his ruling that Corbyn needed “a representative on Earth” to enforce his will. The Labour leader turned to Karie Murphy, his combative chief of staff, to fill that role. That change is credited within Corbyn’s inner circle for sharpening up the operation and preparing the ground for the “brilliant defeat” of 2017, when Labour increased both its votes and its parliamentary presence in the general election, and created a hegemonic position for Corbyn at the top of the Labour Party.

That has implications for Kerslake’s second significant piece of work: his briefings to Team Corbyn about preparing for government. Although Kerslake is not a Corbynite or anything like it, he impressed the team with his knowledge and a shared aversion to written – and therefore, leakable – notes. A fear of deliberate or accidental leaks is why Seumas Milne has urged Corbynites on the party’s ruling National Executive Committee to communicate through Signal, where users can set a time limit before messages vanish after being read, rather than the more popular WhatsApp, where messages linger in perpetuity and can be screenshotted and sent to journalists.

Where Kerslake is less influential is on Brexit. He is a signed-up supporter of the People’s Vote campaign, which demands another In-Out referendum, and has said on multiple occasions that he regards Brexit as an exercise in damage limitation. On that, he and Team Corbyn agree: it’s just when Kerslake talks about damage limitation he is referring to the effect on the country, while Labour strategists mean the effect on the party’s electoral coalition.

There are sound reasons for their concern. Yes, most Labour voters, the vast bulk of Labour party activists and the overwhelming majority of Labour MPs backed a Remain vote. But around a third of the party’s 2017 voters did not and its target seats at the next election are mostly Brexit-inclined.

Until now, when Corbyn has been forced to clarify the party’s ambiguous Brexit position, he has repeatedly chosen to alienate Remainers rather than Leavers. That is because enthusiasm for Labour in general and Corbyn in particular is strongest among the groups – ethnic minorities, social liberals and university graduates – who are most likely to have backed a Remain vote in 2016. Support for Leave is at its strongest among the groups that backed the party grudgingly, if at all, in 2017. He has been banking on reserves of goodwill from the Europe-loving half of his electoral coalition.

Added to this raw electoral calculation, there is no majority in parliament to rerun the 2016 referendum. Opposition comes from three sources: Brexiteers who fear defeat in a fresh contest; pro-Remain MPs who fear that backing a replay means risking their seats; and those from both sides who worry that rejecting the 2016 result looks like contesting “the will of the people”.

Taken together, the electoral and ideological arguments have pointed Labour in the same direction: away from supporting another referendum and towards facilitating some flavour of Brexit. Practical and pragmatic considerations mean that Labour’s preferred Brexit is several degrees of magnitude softer than the one on offer from Theresa May.

So what changed this week to prompt Corbyn to announce his support for another vote if Labour’s proposed deal, including a customs union, fails to pass the Commons next week? The answer is simple. The creation of, and astonishing surge in the polls for, the Independent Group (TIG).

The public “line to take” for Labour loyalists is that this is simply the natural progression of the party’s conference position, which held out the possibility of another referendum as an insurance policy should parliament be unable to agree a Brexit deal and Labour fail to trigger a fresh election. Several shadow ministers have gamely tried to sell that line to me, although they were all conspicuously silent in shadow cabinet on 26 February when a trio of usually loyal Corbynites – Jon Trickett, who like Kerslake works on preparing for government; Ian Lavery, the party chairman; and Richard Burgon, the shadow justice secretary – complained about the policy shift. (Burgon, who is widely believed to be a committed Brexiteer by belief as well as political instinct, asked not unreasonably why he had found out about the change via the press.)

The truth is that parliament is no less deadlocked than it was a week ago. There is no clearer path to a second referendum than there was before Corbyn opted to embrace a fresh vote. The intent of the Labour leadership was that the party’s support for a referendum would remain, like most insurance policies, unused and unclaimed. What has changed is that TIG is a more potent electoral threat than the Liberal Democrats. Compromising on Brexit may have cut off the flow of recruits from the parliamentary Labour Party to TIG – for now.

Corbyn might have stemmed the flow of MPs, but the cost could be alienating Brexit-inclined voters in England. As Lavery once warned, backing a second referendum might mean giving up on any hope of reaching Downing Street. If so, Bob Kerslake’s lessons on how to make Corbynism work in government will be nothing more than a historical curio.