Today regular domestic politics will provide a small interruption to the increasingly frantic attempts being made both by the government and by parliament to seek a way out of the Brexit impasse. A parliamentary by-election is being held in Newport West, following the death of Paul Flynn, a widely-respected MP on the left of the Labour party.

The contest is one that Labour would be expected to win quite comfortably. Nevertheless, the outcome is likely to be examined closely for any clues it may provide as to the impact of the Brexit impasse on the standing of the parties. It is thus an opportune moment to examine the evidence of the polls on that score – not least because we may yet find that the Brexit impasse eventually precipitates a snap general election.

At first glance, it would seem that the debate about Mrs May’s Brexit deal has had remarkably little impact on the fortunes of the country’s two largest parties. When the deal was first unveiled in mid-November the Conservatives and Labour were neck and neck with each other. Now, nearly five months later, the two parties are still neck and neck.

But this does not mean that ‘nothing has changed’. Back in mid-November both parties on average stood at 39% apiece. Now, both are well below that level. The Conservatives are three points down on 36%, while Labour have slipped by four points to 35%. It would seem the Brexit debate has served to erode public confidence in both of the country’s two principal parties of government.

Even more dramatic is the difference between the position in the polls now, and the outcome of the 2017 election, when the two parties’ combined tally of 84.5% of the vote (in Great Britain) was the highest it has been at any election since 1970. Now, the figure stands at just 71%. Britain’s party system is showing signs of fracturing once again.

But, of course, the fact that both Conservatives and Labour have lost ground during the course of the debate about Mrs May’s deal does not necessarily mean that the trend has been occasioned by Brexit. In Labour’s case, in particular, the party has been hit during this period by yet another storm over its handling of anti-semitism, a storm that played a significant role in persuading eight of the party’s MPs to leave and create a new party that is now known as ‘Change UK’. Maybe it is a case of coincidence rather than causation.

One way of trying to establish whether the Brexit impasse has been responsible for the parties’ loss of support is to compare the trend in party support among those who voted Remain with that among those who backed Leave. In the case of the Conservatives, at least, one might anticipate that the party’s difficulty in delivering Brexit would be of greater concern to those who voted Leave, and that the party might have lost ground more heavily among this group than it has among those who backed Remain.

This is, indeed, precisely what we find. On average support for the Conservatives has fallen by six points since mid-November among Leave supporters, while it is unchanged among those who backed Remain. Much of this loss of ground appears to have been to UKIP and/or Nigel Farage’s Brexit party who between them are now registering as much as 7% in the polls. The squeeze on UKIP that occurred in the immediate wake of Mrs May’s decision to call the 2017 general election seems largely to have unravelled in the wake of the Brexit impasse.

In Labour’s case, however, our expectations are not so clear cut. On the one hand, the party’s Leave supporters might be disappointed with the party’s decision to oppose Mrs May’s deal, while, on the other, perhaps Remain supporters are unhappy about the party’s continued relative reluctance to back a second referendum. In practice, it seems as though the party may have lost a little more ground since mid-November among Remain supporters (among whom the party’s support is down on average by five points since mid-November) than it has among Leave voters (down three points). Maybe the party’s attempts to keep both groups on board have failed to satisfy either of them?

That said, there are signs that Labour’s relative success in the 2017 election at winning over Remain voters may be unravelling over the longer-term. At 44%, the average level of support for the party among those who voted Remain is some ten points down on what it was, according to an average of the polls, at the time of the 2017 election. In contrast, the 21% support the party now enjoys among those who backed Leave is just three points down on the position two years ago. If the Conservatives have good reason to be concerned about losing the gains they made among Leave supporters in 2017, it seems as though the Labour party cannot afford to be complacent about the Remain-inclined voters that it won over when the country last went to the polls.