Just in case anyone was concerned that May’s Scottish Parliament election might prove to be a rather dull affair as the SNP marched to a seemingly inevitable second overall majority, two polls, one released by TNS BMRB yesterday and one by YouGov published in today’s Times, have added some spice to the campaign.

Not that they give any sign of a significant diminution in SNP support. TNS BMRB put the party on 57% on the constituency vote and 52% on the list vote, easily enough to give it an overall majority. YouGov’s figures are not quite so good for the nationalists – 50% on the constituency ballot and 42% on the list, both slightly down on where the party stood when the company last polled in October – but again good enough to deliver the SNP another majority.

Rather, the excitement comes from what both polls have to say about the race for second place. Ever since last autumn a number of polls have been suggesting that the Tories were enjoying a modest but noticeable advance, with some companies putting the party at a record high share. The most recent example was a Panelbase poll for the Sunday Times conducted last month. However, TNS BMRB, whose polls, uniquely, are conducted face to face, were not picking up any such advance. Meanwhile, although all polls suggested that Labour enjoyed little more than a fifth of the vote, none had as yet indicated that the Tories had caught Labour up.

Not any more – on both counts. First, TNS BMRB have joined the throng of polling companies showing a Conservative advance. Yesterday’s poll (which was conducted over an extended period in January) put the Conservatives on 17% on both ballots, well up on the 12% (on both votes) that the company reported in January. Indeed, it is the highest the figure TNS has reported for the party since as long ago as 2010.

Unfortunately, however, TNS slightly muddied the waters by deciding to change the way in which they headline their polls. Hitherto they have focused on all those who expressed a vote intention. Now they have opted to focus on just those who say they are certain to vote (some 65% of the most recent sample). If the poll had been headlined on the basis of all those who expressed a vote intention it would have reported a more modest 15% tally for the Conservatives (on both ballots), only slightly better than the 15% (on the constituency vote) and 14% (of the list vote) with which the party was credited by the company at the end of May. However, that still means TNS have now also reported notable progress for the Conservatives – and especially so if we bear in mind that amongst those who were certain to vote in December (that is on the basis on which the latest poll has been reported) the Conservatives only stood at 12% on the constituency ballot and 11% on the list, five to six points down on where they are now.

Nevertheless, TNS BMRB still put Labour ahead of the Conservatives, even though the party stands at just 21% of the constituency vote and 19% of the list tally, little different from where it was in December. But in its latest poll (conducted between Monday and Thursday of this week) YouGov actually put the Conservatives neck and neck with Labour. Ruth Davidson’s party is credited with 20% of the vote on both ballots. Labour, meanwhile, are on 19% on the constituency vote and 20% on the list. Neither party’s tally has changed much since YouGov last polled in October – the Tories are up a point on both votes, Labour down a couple of points on the constituency vote only – but because there was little between the two parties these small movements are enough to close the gap (and also to put the Conservatives on another record high). More broadly, given that no polling company now puts the two parties very far apart, this latest reading certainly adds to the impression that the Conservatives are breathing closely down Labour’s neck.

If that is the case, we can expect the party’s Scottish leader, Ruth Davidson, to claim much of the credit. According to YouGov, slightly more people now think she is doing well as Conservative leader (40%) than reckon she is doing badly (36%). These figures are sharply at odds with those enjoyed by her UK party leader, David Cameron – only 29% think he is doing well while no less than 64% reckon he is doing badly. Perhaps we will not see too much of the Prime Minister during the forthcoming Holyrood election campaign.

Ms. Davidson is even quite well regarded by Labour voters. As many as 46% of them think she is doing well as leader, while just 29% reckon she is doing badly. The Tory leader’s apparent ability to appeal to what is left of Labour’s ranks must be a concern for Kezia Dugdale, whose own ratings continue to disappoint. YouGov’s data suggest that for every voter that Labour has lost since May of last year to the SNP, the Liberal Democrats and the Greens combined, one has also been lost to the Conservatives. In short the Tories are eating directly into Labour support.

Still, YouGov’s poll does contain some hope for Labour – and a warning to the SNP. No less than 53% of all voters – and 66% of those who say they will vote for the SNP – back the idea of increasing income tax in order to improve public services. That, of course, is the ground on which Ms Dugdale decided earlier this week to pitch her policy tent. Indeed, 54% of all voters, including 56% of SNP supporters, also support the idea of increasing council tax in order to improve services. The council tax freeze may be approaching the end of its politically useful life, as well as, perhaps, its fiscally sustainable one. In any event, in proposing a penny increase in the income tax in Scotland in order to fund services Ms Dugdale has apparently hit upon an unexpectedly popular idea for a tax increase.

However, Mr Rennie’s earlier pronouncement that the Liberal Democrats are in favour of a penny increase in income tax to fund spending on education has so far failed to bring his party any obvious dividend, stuck as it is at between 3% and 6% in this latest round of polling. Indeed, it seems unlikely that Ms Dugdale’s position will do her much good either unless she can begin to persuade those who voted Yes to independence in September 2014 that they do not need to follow that up with another vote for the SNP now, as 89% of them still propose to do. Unless that figure comes down Labour are set to remain in trouble.

Yet for all the SNP’s dominance of the electoral scene, the prospect of the party being able to hold a successful second independence referendum still looks like a distant one. Once those who say Don’t Know are left to one side, 45% say they would vote now for independence, exactly the same proportion as eighteen months ago. This is actually the lowest level of support for independence recorded in any YouGov poll conducted since the referendum. The SNP may well win another majority, but, if so, it seems, at the moment at least, that they are going to have to use it to administer another five years of Scotland as part of the Union.