The mixed political legacy of Margaret Thatcher is laid bare in a Guardian/ICM poll that asked voters about a range of her most iconic policies on the afternoon of her death.

Top of the popularity stakes is her drive to sell council homes to tenants. The famous "right to buy" was a vote-winner for Thatcher in her own day, expanding the Conservative constituency to include aspiring working classes, and it remains popular 30 years on – 65% say that this policy worked, as against just 24% who say that it did not.

The defining Thatcherite mission of taking on trade union power was always controversial, but on balance it remains popular too: by 50% to 34% it is deemed to have worked. The independent nuclear deterrent is another battle which the prime minister who pushed ahead with Trident is deemed to have won, by 40% to 28%.

Beyond this, however, the Thatcher prospectus holds less appeal today. Despite suggestions from today's Tory backbench that conflicts with the continent lead to popularity at home, only 38% of voters look back and judge that Thatcher's habit of picking fights with Europe can be said to have worked, as against 39% who say it did not.

On the economic front, the record is mixed – but mostly negative. Her overall shakeup of the tax system splits the country down the middle – the 38% who support the Thatcherite move to increase VAT in order to fund income tax cuts are matched by 38% who say this fiscal switch didn't work.

It's a different story at the top end, however. The sweeping 1980s cuts to top tax rates were sold as unleashing the energy of wealth creators, but they are today judged to have failed by a substantial 47% to 28% margin.

And amid a fresh slump even deeper than that of the 1980s, the Thatcherite macroeconomic mix – namely, putting lower inflation first, and considering unemployment only second – is rejected, by a 41% to 33% margin.

Even more striking is the retrospective rejection of the archetypal institutional reform, the privatisation of utilities such as gas and water – by 49% to 35% Britons say this did not work. Last, and perhaps least surprising, there is the flagship on which Thatcher went down – the poll tax, or more properly the community charge. It is deemed a retrospective failure by a 70% to 14% margin.

In addition to asking about her individual policies, ICM asked voters for an overall assessment of whether Thatcher's 11-year premiership had been good or bad for Britain. Here, the assessment becomes more positive: half of all respondents, 50%, look back on her overall contribution as positive, which is 16 points more than the 34% who say she was bad for the country.

If the overall verdict is kinder than the sum of the policy parts, then it could be because of admiration for Thatcher's character, and additional questions confirm that the public extend her real credit for having become the first female prime minister.

Nearly two-thirds, 62%, say her example played an important part in "changing attitudes about the role in society that women can play", twice as many as the 31% who believe that she changed little about gender relations in wider society "because she played by men's rules".

Women are even more convinced than men of the importance of the Thatcher example: 64% of them think she changed societal attitudes.

Another aspect of the Thatcher story that inspires admiration is her rise from ordinary origins. ICM finally asked respondents about whether or not someone like Margaret Thatcher, a grocer's daughter, could rise to the top of today's Conservative party, which internal critics sometimes suggest is run by "posh boys".

David Cameron, the old Etonian in charge of the party, will be relieved to learn that by 51% of voters do believe that Margaret Thatcher could still get to the top today compared with 34% who do not.

The poll's small print provides evidence that a woman who divided opinion in life continues to divide it in death. In rating her overall record, opinions remain strong on both sides: half of her admirers, 25%, rate her record as "very good", and most of her detractors, 20% of the overall sample, deem it to have been "very bad". Indeed, only 11% sit on the fence and say she was "neither good nor bad"; an even smaller slither of opinion, just 5%, told ICM that it didn't know.

There are also marked divisions across different parts of the population. The old are keener than the young, with 64% of pensioners rating Thatcher as good for Britain as against just 39% of 25- to 34-year-old voters, a demographic that remained in childhood when she stepped down in 1990. The split in opinion over the woman who promoted a home-owning society is even sharper across families with different types of tenure: 63% of those who own their own property outright admire Thatcher overall, as against just 24% of tenants in council homes.

There is a steep class gradient in affection for the woman who spoke in private about parts of the electorate being "our people": 60% of the professional AB social grade judge her as having been good for Britain, as against just 40% of respondents in the lowest DE occupational grade. Naturally, there is also a strong party split: fully 90% of Conservative identifiers regard her record as good, as against just 24% of Labour leaners.

When it comes to the Thatcher record as opposed to the Thatcher example, women are marginally less keen than men – 48% rate her as a force for good compared with 52% of men. More substantial, however, are the regional and national splits over the woman who is often accused of inflaming the north-side divide. More than half (55%) of English voters rate Thatcher as having been good for Britain, compared with 34% of the Welsh respondents questioned, and just 23% of Scots. And within that overall English score there is another divide: in the south fully 60% of voters judge her record as good against 47% who say the same thing in the north.

ICM Research interviewed a random sample of 965 adults aged 18+ online on the afternoon of 8 April 2013.