It was the best line in her Observer article that clinched it. "YouTube if you want to," wrote Hazel Blears on Sunday. "But it's no substitute for knocking on doors or setting up a stall in the town centre."

The echo was intended. And it was completely unmissable. On October 10 1980, Margaret Thatcher had made a defiant speech to the Tory conference in Brighton. It contained a line that still defines her nearly three decades later. "You turn if you want to," she said. "The lady's not for turning."

As a piece of explicit, self-aware political homage, Blears's line could hardly have been more obvious or – given Thatcher's massive political achievements and iconic status – more audacious. It emboldens me to suggest an idea I have been mulling for some time. Here it is. Hazel Blears may just have it in her to be Labour's Margaret Thatcher.

The parallel is not as crazy as it sounds. Think about the comparisons. First and most obviously there's the gender issue. Yes, they are both women. Like most successful women in a predominantly male political culture, they have spent their early ministerial careers being mercilessly patronised – Thatcher for being a Tory housewife, Blears for being a Labour cheerleader. But because Thatcher was both so readily patronised, she was also seriously underestimated. The same is true of Blears – as George Monbiot is the latest to discover.

Thatcher, a woman from a Methodist upbringing who qualified as a lawyer before becoming an MP, was always a much smarter and braver politician than the men in her party ever realised – until it was too late. Blears has not run for the Labour leadership yet, and maybe she never will, but she too is a woman with a Methodist background who is also a qualified lawyer and now an MP. And she is certainly much smarter than she is given credit for. She may prove to be a brave politician too – if the Observer article is anything to go by.

The comparisons go further. Thatcher always prided herself on having a gut feeling about "our people", by which she meant hard-working, law-abiding, aspirational Tory voters from the London suburbs. Blears has an almost uncannily comparable sense of connection with her own voters. Except that in her case she means hard-working, law-abiding, aspirational Labour voters from industrial Lancashire.

Thatcher always had a profound sense of being an outsider, about not being a member of the London establishment. Blears has a very similar sense of being rooted in Salford and not being part of the metropolitan elite either. (It is one of the things that in turn distinguishes Blears from that other Labour woman solicitor turned minister, Harriet Harman – it is no secret that the two Labour women, the one northern and working-class, the other southern and middle-class, are not political sisters).

After some dire performances early on, Thatcher managed to fuse her ambition with her other formidable qualities into a potent populist mix which most of her own party adored and which her opponents loathed. It was a combative brew that enabled Thatcher to blast through every political glass ceiling. At 53 she became Britain's first woman prime minister, 30 years ago this week. Blears has made some people cringe on her way up – just as Thatcher did. But could Blears, 53 this month, do for Labour what Thatcher did for the Tories? I wouldn't rule it out at all.

Labour's and Blears''s situations today are, of course, very different from that of the Tories when Thatcher ousted Ted Heath in 1975. Most obviously of all, the Tories were in opposition while Labour is still, just about, in government. And Blears will never simply be some inverted image of Thatcher. Politics isn't like that. Nor are people.

Yet if you look at the Labour party today and try to imagine a current minister of either sex with unchallengeably authentic political roots, an aspirational life story that image makers dream of, a clear sense of where she's coming from, an irresistible confidence in her own instincts, a clear set of convictions, and the potential to turn herself into an iconic political figurehead, you don't find many better candidates than Blears.

I doubt if many people have considered Blears as a truly major political figure. She isn't even mentioned in those lists of odds from Ladbrokes about Gordon Brown's successor. But that was true of Thatcher too. When Thatcher challenged Heath, she was mocked and underestimated. British politics in the 1970s didn't know it at the time, but it was ready for a good woman leader. No one laughs at Thatcher now. Something similar may be true today – and that good woman leader, if she plays her hand well and audaciously, could just be Hazel Blears.