TNS also found that a quarter of all voters were still undecided as to how they would vote on 7 May – including those who state they are certain to vote.
TNS also found that only 64% of voters were certain to vote in May, in contrast with the 85% turnout in September's independence referendum.
TNS speculates that this attitude reflects the difficulty of switching employers rather than genuine loyalty; it talks of "captive" employees.Such averages mask wide variation, of course.
The TNS poll gives the SNP a 10-point lead over Scottish Labour among those certain to vote, at 41% against 31%, putting nearly half of the 41 Westminster seats won by Scottish Labour in 2010 at risk.
TNS, which is regarded as more cautious than other pollsters, said its findings suggested the gap between the SNP and Scottish Labour is much narrower than the 20-point lead given to the nationalists in a spate of other recent polls, but that it was still gloomy news for the Scottish Labour leader, Jim Murphy.
They also echoed the sudden sharp rise in yes support in the closing weeks of the campaign, and confirmed what YouGov and TNS BMRB had discovered: that the referendum vote was too close to call.
Tom Costley, the head of TNS Scotland, said the polling also suggested the SNP were peeling off voters disaffected with the Liberal Democrats as well as former Labour voters most frequently identified as SNP converts after Nicola Sturgeon became party leader and first minister.
Related: Inside the campaigns: 'The argument about Trident isn't really about Trident' Labour recorded a six-point lead over the Conservatives in a Panelbase poll; it was four points clear in a Survation survey for the Daily Mirror; and three ahead in a TNS poll.
A third poll, by TNS, is due tomorrow.
According to TNS Sofres, another pollster, 68% of the electorate supports the constitution.
TNS, a research firm, says a quarter of British shoppers claim to be willing to pay more for clothing that comes from firms that pay their employees fair wages or protect the environment.
