The Brecon and Radnorshire by-election on August 1 is likely to be the latest demonstration of the depths of electoral crisis the Labour Party finds itself in. It is a seat that is regularly portrayed as a close contest between the Liberal Democrats and the Conservatives, but its electoral history is far more complex than that.

The 2017 election win for Conservative Chris Davies saw him increase his 2015 majority of 5,102 to 8,038. That 2015 result was the largest since 1983. The intervening years were a story of variable electoral marginality. However, it hasn’t always been a seat of Lib Dem strength. It has actually had more Labour MPs than MPs of any other party – something which tells its own story of Labour decline since it last won the seat in October 1974.

So, what of Labour now? What does it stand for? And what does its positioning on Brexit and accompanying political messaging say in the context of the Brecon and Radnorshire by-election?

Labour’s Deputy Leader, Tom Watson MP, has urged members to sign a public declaration calling for Labour to be ‘the party of remain’. The Welsh Labour Party’s leader Mark Drakeford AM has been clear on his pro-further referendum and pro-remain position. Yet those who proudly already identify as remain parties have coalesced around the Lib Dem candidate in a nascent remain alliance. Is the ‘party of remain’ also backing this remain alliance? Of course not. Labour’s tribal character hard-wires it against electoral co-operation and so it is running.

Meanwhile, in an election that will receive media coverage that will be as much national as it will be local, Corbyn continues his position of ‘constructive ambiguity’ or, as the New Statesman puts it, ‘destructive ambiguity’. The language is still of a ‘public vote’, still maintaining that a general election is preferable to a further referendum even when Labour is polling at its most disastrous level since polling began. There is no indication yet, despite increasingly frantic calls from Labour loyalists, that if they did secure a further referendum that Corbyn would campaign for remain. Instead, Labour’s either/or way forward risks further frustrating those that want a clear commitment to another referendum and remain, those who see a General Election as a route to uncertainty and/or annihilation, and those who want to see Labour deliver Brexit.

Some in Labour will indignantly protest that Labour is a party of remain, but that it is also seized with dealing with the very real and wide range of societal problems Tory austerity has caused. That is fair comment, but think about that, and Labour’s Brexit positioning, in the context of this by-election.

If Labour had stood down, co-operating with the Lib Dems, it would have been a tacit admission that it was not capable of standing on its own remain credentials. It would also demonstrate that the Lib Dems are the party of remain for the purposes of this by-election, bolstering their credibility in the first electoral test of a new Conservative Prime Minister, held just days after that PM takes office.

As it is, Labour is running, possibly as a remain party (taking its cue from Drakeford and Watson), possibly not (taking its cue from the Milne, Murray, McClusky, Murphy tendency around Corbyn). Whatever, it is clearly not remain enough to back a remain alliance. So, when it gets electorally hammered, its irrelevance as a party of remain in a seat it has represented more than any other party will have been demonstrated – along with the fact that it cannot cope with the co-operative instincts of many Remainers.

What if Labour makes the case that there are more important things than Brexit, maintaining its position of constructive ambiguity, hoping to talk about other critical issues such as the impact of Tory austerity? That Brexit isn’t the all-defining issue the commentariat – or hated mainstream media – think it is? That is fine until the public votes along Brexit lines – for the Brexit Party and the Lib Dems – confirming that, in reality, Brexit is the issue that matters to them most.

In the end, the Brecon and Radnorshire by-election – combined with the local elections and the European election – is likely to demonstrate the catastrophic folly of predicating a strategic position on Brexit on a tactical electoral position of constructive ambiguity, which is necessarily limited in its ability to speak to the long-term and the much-sought certainty that voters are desperate for.

The electorate are not stupid. They know that politics is about more than Brexit. But they are also realising that the defining battle-lines in the Brexit debate represent broader world views about society, the future, the past, and Britain’s position internationally. They then see that the party-political landscape, which informs and is informed by an electoral system, a media, and political institutions that service binary narratives, and which hitherto has entrenched the interests of Labour and the Conservatives, is shifting axes – and they are picking sides.

By failing to pick a side, Labour are in the process of rendering themselves irrelevant.