Voters in Falkirk say there has been a significant shift of mood in recent weeks, and some see a chance to make history

"It's not always a bad thing to take a chance," says Michelle Stafford, a carer with five young children, who is waiting outside Greggs on Falkirk High Street while her partner, Scott, buys sausage rolls.

"I like the positivity of the yes campaign. I'm voting yes because I feel Scotland could do better under a Holyrood government that is more in touch with the country's needs."

Stafford is one woman in a surge of female voters, long doubtful about independence, who are now swinging towards yes in the final weeks of the referendum campaign. A TNS poll confirmed the trend on Tuesday, with the proportion of women planning to vote yes on 18 September rising by eight points in the space of a month, to 35%.

Stafford has never voted before, although she describes her family as strong Scottish Labour. She reached her decision in the summer after reading parts of the white paper and researching questions about the NHS online. As such, she is part of another trend that has defined this campaign: ordinary Scots looking beyond the soundbites on either side and informing themselves about the issues that matter.

It's the little things that have convinced her, she explains. Scott rang up the distributors of Buckfast after reading an article on Facebook a warning that Scotland's favourite tonic wine, brewed in Devon, could not be imported after independence. The woman who answered laughed down the phone at the suggestion.

"All those big companies that are threatening to relocate, but do they really want to lose all their Scottish customers?" asks Stafford. "The more scare tactics they use, the more I'm put off voting no."

As working class and Labour voters likewise swing to yes, it is this fundamental credibility gap that the no side must bridge in the final days of campaigning. Those dire warnings about Scotland's economic prospects after independence, which have long been its focus, appear to have stopped working. Last weekend's YouGov poll reflected an increasing optimism among voters about how well off they would be in the event of a yes vote, with more than half believing that Westminster is bluffing over a currency veto.

Tuesday's statement of a timetable for further devolution powers, and emergency dash by party leaders from London, is too little too late, according to voters in Falkirk. "The Westminster parties are panicking," says Leanne Oliver, a social care worker in her 30s, who remains undecided. "They should have taken this referendum seriously long before now."

Oliver, a Labour supporter, is especially critical of her own party's role in the campaign, dismissing Gordon Brown's announcement on Monday night of fast-track powers. "There's nothing new coming out. He's telling us what they were going to give us anyway." The Labour no campaign hasn't been successful at all, she says. "Basically, they've been trying to frighten us."

Lissa Orr, 36, previously a Labour voter and now a Green party supporter, is similarly disappointed with Labour's role in the referendum. Feeding her four-year-old son a yoghurt in the Howgate shopping centre, she explains: "Being in with the Tories hasn't helped. It's like they've forgotten their roots in Scotland, which has always been a Labour stronghold."

A yes voter, Orr adds: "I'm not an SNP supporter but Nicola Sturgeon puts a much more positive case for women. In terms of families, I don't believe anything Labour tells us." (The Labour no campaign this week is noticeably male dominated, with Ed Balls, Gordon Brown and John Prescott centre stage.)

She mentions the pro-union Better Together advert aimed at undecided women voters that was slated two weeks ago as patronising and sexist. "The no campaign doesn't reflect modern women or modern times."

She challenges the received wisdom that Brown holds particular traction with Labour voters in Scotland. "Gordon Brown is not in government, so he's in no position to make promises. Even with my in-laws, who are Labour and strongly no, they remember what he did to the economy when he was in power."

Amanda McMillan is crocheting by her sweetie cart at the other end of the precinct. An SNP voter and long-time supporter of independence, she, like all the other voters I speak to, describes a significant shift of mood in the past few weeks. "Honestly, I thought the noes were going to get it," she says, "but in the last few weeks I've noticed a definite shift."

She times it to the last STV debate, with its cross-party panel including the comedian Elaine C Smith and the Green party MSP Patrick Harvie for yes. "Because a lot of people were thinking this was just about Alex Salmond. I've seen opinions change, just through talking to people in the shops around here.

"I'm voting yes because I feel we have the chance to make history, and to govern ourselves. We're getting something with a tick in a box that other people are fighting and dying for. We have the chance to do it peacefully."