Pressure is building on Labour to shift its Brexit stance. Owen Smith’s demand that the party should back a second referendum led to him losing his job. But there are growing calls for the party to adopt a less ambivalent position, either in favour of single market membership or of a second referendum. These arguments are framed as a statement both of principle and electoral common sense – the influential mayor of Liverpool, Joe Anderson, has argued that insisting on a further Brexit vote would place Labour “on the right side of public opinion”.

And there is apparently some polling evidence to back this up. A December 2017 survey for YouGov, commissioned by Best for Britain, found that 24% of voters currently planning to support Labour might change their minds before the next election. A few months later, another such survey suggested the Liberal Democrats would surge (in relative terms) to 18% if Labour and the Conservatives remain committed to leaving the EU.

Clearly such figures should be treated with some caution. It is quite hard to foresee an election between now and 29 March 2019, when the UK is due to leave the EU. Not least, the mechanics of the Fixed-term Parliaments Act make it a difficult outcome to engineer. Moreover, there is clearly a question as to whether the Labour leadership actually believes in the value of questioning Brexit.

Yet let’s leave aside whether a party recently characterised as made up of “remainers outside of Westminster led by Brexiteers within it” would favour a policy shift away from leaving the single market, or even the EU itself. Does Labour have anything to gain electorally by shifting in this direction?

Labour policy on Brexit has been driven as much – indeed more – by short-term politics as by concerns about the nature or depth of the future trading relationship between the UK and the EU. Consequently, the positions the party has adopted have generally consisted of soundbites designed to give the impression of distance from the government’s stance.

Jeremy Corbyn’s oft-repeated line that Labour wants “tariff-free access to the single market” sounds good to many of those with better things to do than study single markets, while being utterly devoid of meaning. Labour’s “six tests for Brexit” set out by Keir Starmer, not least his call for the maintenance of the “exact same benefits” of the single market, is as politically savvy as it is divorced from reality. Nowhere is it specified how Labour would pull off this trick.

Recent policy shifts over potential membership of a customs union should be interpreted in the same political light. The Labour leadership saw the prospect of inflicting a humiliating defeat on the government. And this defeat on a customs union is now likely, sooner or later, on an amendment to the trade bill after the local elections.

Yet it is interesting to note the trouble Corbyn went to to triangulate his position. He refrained from committing entirely to “a new comprehensive UK-EU customs union”. Rather he insisted that, in order to accept such a deal, the UK would need to have a say over future trade deals, something on which the EU has blown hot and cold in the last few days. Moreover, he emphasised that Britain would no longer accept freedom of movement, and hence would be leaving the single market.

So ambiguity has been the chosen approach for Labour. And it has worked. What colleagues have labelled Brexit Blairism has proved electorally highly effective. As this table shows, Labour picked up vote share across the board in both leave and remain constituencies.

Now, however, as the moment of Brexit truth approaches, many are claiming that Labour must make a clearer choice and come out more unequivocally for a far softer Brexit than the government seems to want. Implicit here is the assumption not only that this would be the “right” thing to do, but that it would be electorally advantageous.

This, however, is far from self-evident. Consider the figure below. It maps every constituency in England and Wales. To the left are those seats that swung disproportionately towards the Tories in 2017 and to the right are their Labour equivalents. In the top half are seats that went majority remain, while under the line are majority leave seats. Highlighted – in red and blue respectively – are seats where Labour or the Tories have a majority of less than 5% to overturn. These are, in other words, the target seats that really matter to party strategists.

What is apparent is the relative lack of Kensingtons or Canterburys waiting to fall to a Labour party expressing clearer opposition to Brexit. Justine Greening’s seat of Putney – which voted 72% remain and swung 10.23% to Labour last time – is one of the few red dots in the upper righthand quadrant. Of the 15 seats where Labour has the smallest margin to close, only two – Pudsey and Chipping Barnet – voted remain. In total, there are just 12 constituencies that voted remain where Labour require less than a 5% swing to win next time.

Moreover, it is in the bottom right quadrant – places where Labour gained more than average on the Conservatives last time, and that voted leave in the referendum – where the highest number of potential Labour gains are clustered. These are places, in effect, where their Brexit strategy in 2017 hit the electoral sweet spot. Labour needs to gain 34 seats for a majority of one at the next election. Of the 34 seats in England and Wales where they are running closest behind the Conservatives, there are more seats that are estimated to have voted over 60% to leave than to have voted remain.

Equally, there are places – principally in the bottom left of the graph – where Labour are vulnerable if the relatively small, but crucial, number of ex-Ukip supporters break off from their electoral coalition. The 10 Labour seats where the Tories have to do least to win next time round voted, on average, 63% leave. These are places where we might expect the Tories to pour a lot of resources, places such as Bolsover and Wakefield.

Brexit created a shift in our electoral geography. Most voters didn’t shift their allegiances due to Brexit. But enough, in some key places, did. Labour capitalised on this in 2017 via a position of strategic ambiguity. Whether this success was the result of deliberate policy or of blind luck is something for future historians to argue about. What matters here is the future.

And here the choice is relatively stark. Labour can either continue as it has to date, with continued incremental policy shifts keeping its position slightly softer than that of the government while still “respecting the referendum outcome”. Flexible ambiguity, in other words. Or, the party can break with its ambivalence and support either a Norway-type deal or – more ambitiously – a second referendum. For all the obvious hope out there that the party will choose the latter, the electoral maths seems to militate in favour of the former.

• Anand Menon is director of the UK in a Changing Europe and professor of European politics and foreign affairs at King’s College London