Almost inevitably, the SNP conference has occasioned something of a flurry of polling. After nearly three months without any polls of voting intentions in an election or any future independence referendum, yesterday two polls commissioned by newspapers were published, one by Panebase for Sunday Times Scotland, and one by Survation for the Sunday Post In addition, the SNP released the details of some polling that they had also commissioned from Survation, though undertaken over the phone rather than online.

Much has happened in the last three months. Alex Salmond has taken the Scottish Government to court. The Scottish Government’s policy of testing P1 pupils was voted down at Holyrood. Meanwhie, the debate about what Brexit should or should not mean has continued to rage. Yet, according to the weekend’s polling it seems that none of this has had much impact on the balance of public opinion north of the border.

So far as voting intentions in a UK or a Scottish Parliament election are concerned, the two newspaper polls for the most report at most only small, statistically insignificant one- or two-point changes in party support as compared with the last poll conducted by the same company for the same newspaper. There is just one exception – an across the board three-point drop in Labour support since the previous Panelbase poll for the Sunday Times last June.

That drop was not replicated by Survation. However, that company had already registered a fall in Labour support in its previous poll in July. Both polls agree that Labour are on just 24% support for Westminster, though the poll conducted by Survation for the SNP put Labour on 26%. Still, even taking that reading into account Labur’s average reading in the three polls is 25%, two pints down on what the party secured in last year’s general election (and two points below the average of 27% recorded for the Conservatives.

In contrast, the three polls put SNP support in a Westminster election either at (in the case of the party’s own poll) or slightly up a little on the 37% it secured in 2017 (in one instance by just one point, in the other by four). As a result, the party’s average score is 39%, up two points on 2017.

(Parenthetically, we might note that while the two newspaper polls suggested there had been little or no change in the level SNP support for a Scottish Parliament election, at 44% on the constituency vote and 40% on the regional ballot, the poll conducted for the party by Survation gave the party its highest share in any poll of Holyrood vote intentions since March 2017. Even so, at 43% and 36% respectively, the party’s average rating for the two ballots across the three polls is still four and six points respectively what the party secured at the last Scttish Parliament election in 2016, which means that there will continue to be a nagging question at the back of Nicola Sturgeon’s mind as to whether, even with the support of the Greens (on 7%), there will still be a pro-independence majority at Holyrood after 2021.)

Small though they are, these seemingly minor movements since last year’s general election potentially matter. Many of Scotland’s Westminster constituencies are highly marginal, and as a result, the outcome of the next UK election north of the border potentially has profound implications for Jeremy Corbyn’s chances of winning an overall majority. A small swing from the SNP to Labour could see Labour make significant gains, and help Mr Corbyn claim the tenancy of 10 Downing St. But a small swing from Labour to the SNP, as registered in these polls, could see Labour losing some of the gains that it made last year, and make it more likely that the SNP holds the balance of power after the next Westminster contest. And, of course, there is at least a remote possibility that the next Westminster election might come sooner rather than later, should the UK government be unable to secure the support of the House of Commons for whatever Brexit deal it manages to conclude.

But when it comes to the question of Scotland’s constitutional status, there is again little sign of a change in the balance of opinion – for the time being at least. After excluding those who did not know how they would vote in a second independence referendum, Survation’s poll for The Sunday Post put support for Yes to independence at 47%, the same as in its previous poll in July. Panelbase, in contrast, put support at a more modest 44%, but again the figure is exactly the same as in its previous poll. Meanwhile, Survation’s poll for the SNP is reported to have come in between these two figures at 46%. All in all, there is little here to disturb the conclusion that support for independence remains at more or less the 45% level that was registered in the 2014 referendum. Indeed, the average level of support for independence registered by all ten readings published this year is 45%.

Nevertheless, there was still one source of excitement in yesterday’s polls – the responses to questions about how people might vote if Brexit does happen in one form or another. Given that the current level of support for independence in the polls is not far short of 50%, only a relatively small number of people have to tell the pollsters that they might vote differently in response to some hypothetical set of Brexit circumstances for the 50% mark to be reached. Thus, when in its poll for the SNP Survation asked people how they would vote if the UK does leave the EU, 50% said that they would vote Yes, 50% No – a 4% swing from current vote intentions that is not dissimilar to the 3% swing registered by YouGov in a similar exercise for Best for Britain in August. This picture is broadly corroborated by the Survation poll for The Sunday Post, which found that 16% of those who voted No in 2014 say they would be more likely to vote Yes if Brexit happens, while only 10% of 2014 Yes supporters say they would be less likely to do so – figures that again imply that Brexit could generate a 4% swing.

Not surprisingly, perhaps, posing the prospect of a ‘no-deal’ Brexit in particular does nothing to reduce this hypothetical swing . Panelbase found that in these circumstances, 48% would vote Yes, 52% No (after excluding Don’t Knows) – a 4% swing to Yes as compared with current vote intentions in the same poll, though a significant proportion of the swing is generated by the 16% of current No supporters who say they do not know how they would vote in the event of there not being a deal (just 3% said they would switch to Yes, while 3% of Yes supporters say they would move in the opposite direction) . Meanwhile, Survation’s poll for the SNP found that 52% said that they would vote Yes in such circumstances – a 6% swing as compared with how people in that poll say they would vote at present.

In truth, polls of hypothetical vote intention have to be treated with considerable caution. Not least of the reasons is that not only do they rely on the ability of voters to anticipate what they might do in a particular set of circumstances, but they also invite respondents to focus on one particular aspect of the independence debate when in reality voters’ views will reflect a variety of considerations. They are, perhaps, at best regarded as an indication of the likely maximum extent to which attitudes might shift if the hypothetical circumstances were to arise. If in the event there is something of a shift, then when the Brexit process has come to some kind of conclusion and Nicola Sturgeon, as promised, does indicate what she would like to do about holding indyrerf2, she might be looking at a set of polls of vote intentions that look a little more promising for Yes than they do at present. Even so, it seems that she is unlikely to be left with anything other than a tough decision.