During the past month of unusually dry weather, the referendum polls have been as stagnant as some of the nation's ponds but, with recent rain, has come a shift.

The lead of the No campaign shows signs of being eroded by a surge in support for Yes among Labour voters.

The change relates only to one poll but it is significant that it is a TNS BMRB poll, that company not being known for overestimating the extent of Yes support. According to TNS, support for Yes is up three points and that change appears to be due to the campaign's success in winning significant support from people who voted Labour in the 2011 Holyrood election. Overall, compared to TNS's last poll, the No lead has shrunk from 18 points to 12, excluding don't knows.

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The SNP have been alive to the need to win over traditional Labour supporters for months and, if this poll can be trusted, their appeals to that group are paying off. Nicola Sturgeon made a high-profile plea to Labour supporters in her keynote conference address in April, promising that the Yes campaign was not asking them to leave their party and support the SNP but to "reclaim" their party through Scottish independence.

It will be of particular concern to Scottish Labour that TNS's poll was conducted during a period when the UK Labour leader, Ed Miliband, was in Scotland for a high-profile visit in support of Scotland staying in the Union, during which he contrasted Labour's credentials as the party of the poor and the low paid with the SNP's. He brought with him several members of the Westminster Shadow Cabinet. Meanwhile, the former Prime Minister Gordon Brown has stepped up his role in the campaign, appealing heavily to Labour supporters, and Labour MP Jim Murphy has been touring Scotland on behalf of Better Together. Privately, Labour will be concerned these heavyweight interventions aimed at the party's heartland are failing to win hearts and minds, and that some traditional Labour voters could be having their heads turned by Yes Scotland instead.

There are several possible reasons for this. Previous polling shows that more Scots would be slightly more likely to vote Yes if they thought the Conservatives were going to win the next General Election but more voters would reject independence if they thought Labour would win. While the Tories are still behind in the polls, there are more than nine months to go and Ed Miliband continues to weather slings and arrows about his leadership, most recently from former Labour Home Secretary Charles Clarke. It is also possible that voters feel alienated by the Westminster establishment after weeks of coverage about threats from certain Conservatives to withdraw from the EU.

Whatever the reasons, this latest poll will act as a reminder to Better Together that, in spite of its continuing lead, complacency now would be highly dangerous. There is some comfort for the No camp: Yes Scotland appear to be lagging as much as ever among women and, in any case, one poll does not make a trend. Even so, the referendum race looks as if it has become more interesting again.