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. The sale of council homes and tackling of trade union power remain popular today, but people are less supportive of the fights she picked with Europe and tax cuts for the rich. Privatisation of the utilities and the poll tax remain deeply unpopular.

ICM also 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.

Graphic: Guardian

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".

Graphic: Guardian

When ICM 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", 51% of voters believe Thatcher could still get to the top today compared with 34% who do not.

Graphic: Guardian

There are also marked divisions across different parts of the population. Older people 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 still in childhood when she stepped down in 1990.

The class divide is also stark: 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-south 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.

Allowing council tenants to buy their homes

Graphic: Guardian

Thatcher's most popular idea was not a total novelty: it was played with by Edward Heath's government, and even featured in the 1959 Labour manifesto. But it was under Thatcher that government legislation in 1980 replaced local experiments with a nationwide drive, which saw a million homes sold by 1987. Substantial discounts combined with a buoyant property market to make the scheme profitable and popular with the tenants who took it up. But as it was combined with the virtual cessation of council housebuilding, it led to a shortage of supply and today's extraordinarily long housing lists.

Taking on trade unions

Graphic: Guardian

Membership was at its peak as Thatcher arrived at No 10, covering half the workforce – and with these numbers came a controversial clout. After the Heath government's attempt to pass a tough new law, the Wilson-Callaghan government negotiated swaths of policy with the unions, but both administrations were ultimately brought down in the aftermath of strikes. Thatcher was determined to tackle the unions, but also to avoid the fate of her predecessors, and so she resolved to fight smart. She took on strikes one sector at a time – waiting until the favourable circumstances of 1984 for her great showdown with the miners. Likewise, the legal restrictions – regarding internal structures, requirements for ballot, the closed shop and secondary action – came in a succession of bills, as opposed to one big bang. Taking on everyone at once, today's coalition arguably lacks the Thatcherite sense of how to sequence the fight.

Investing in Britain's nuclear deterrent

Graphic: Guardian

Almost as much as the industrial "battle of Orgreave", the 1980s is remembered for the tussle between the peacenik women of Greenham Common on the one hand, and – on the other – the lady who was famously photographed in the tank. Following the Soviet invasion of Afghanistan, the "second cold war" of the early 80s was a time of renewed rising international tension after the 1970s detente. The previous Labour government had in fact retained Britain's nuclear bomb and already committed to rising defence spending, but Labour took a unilateralist turn in opposition, which Thatcher defined herself against by welcoming American cruise missiles and moving to upgrade Trident. Previous polls have suggested the public is no longer convinced of the value of nuclear weapons, but it is perhaps because Thatcher's stridency on the nuclear question came before the collapse of communism that it is today retrospectively regarded as a success.

Picking fights with Europe

Graphic: Guardian

Pro-Europeans point out Thatcher campaigned for a Yes in the 1975 European referendum, and that she went on to sign the Single European Act as PM. All that is true, and it underlines that she was more a creature of her times than is sometimes remembered today, but as a rightwing Tory with a certain imperial nostalgia she was never entirely at home with Europe, and picked fights almost from the off. Very early on, she went to Brussels, waved the handbag and came back with the British rebate. Later, as her views hardened, she found herself at loggerheads with Europe again and again – resisting federalism in favour of a Europe of separate nation states in the Bruges speech, and deeply reluctant to enter the exchange-rate mechanism, until she finally caved in right at the end. Even in the happy circumstances of the collapse of communism she created conflict, by warning against German reunification.

Cutting income tax while raising VAT

Graphic: Guardian

During the late 1970s, the Conservatives complained a great deal about taxes on income being too high, but they said much less about what they would do to fund any reduction. The answer became clear almost immediately after the 1979 election, when a cut in the basic rate of income tax from 33p to 30p in the pound was matched by a near doubling of VAT from 8% to 15%. The immediate effect was inflationary, and there is little economic reason to believe that people will work harder if you allow them to keep more of their earnings, but then tax almost everything these earnings can buy. Nonetheless, this shift in the tax base stuck, with VAT eventually rising to 17.5% under John Major and 20% under the coalition, while basic-rate on incomes steadily fell under governments of different stripes towards today's 20p.

Cutting top tax rates for the rich

Graphic: Guardian

An early Thatcher priority, the top rate on earned income was cut from 83% to 60% at a stroke in 1979. In 1988, chancellor Nigel Lawson went much further and abolished all rates above 40%. Bitterly resented by leftists at the time – Alex Salmond's fury in the Commons during the debate caused him to be suspended from the House – but with New Labour's promise that there would be "no rise in income tax rates" it seemed as if Thatcher had forged a lasting consensus on a tax system that ensured handsome rewards for entrepreneurs and other top earners. After the financial crisis hit, however, Labour had a rethink and raised top tax again. George Osborne's move to cut it last year turned into a political disaster, and today's poll suggests that this is an aspect of the Thatcher record which meets with the opposite of consensus today.

Putting the fight against inflation ahead of the fight against unemployment

Graphic: Guardian

Perhaps the defining feature of Thatcher's first term was to break with the postwar consensus on the need to maintain full employment. The second oil shock took hold in the aftermath of the Iranian revolution and catalysed a vast shakeout of heavy industry, with the loss of millions of jobs. All established wisdom said that something would have to be done, but Thatcher cut public spending, maintained interest rates and even increased tax. A decade before, unemployment of 1 million was considered unacceptable but – more concerned to achieve stable prices than anything else – Thatcher persisted with austerity until the dole queue reached thrice that. Inflation did fall, interest rates followed and so, eventually, did unemployment. But male worklessness in particular has never since become the rarity that it was in pre-Thatcher days.

Privatisation of utilities such as telecommunications, gas and water

Graphic: Guardian

The Conservatives had always believed in private industry, and had previously reversed Labour nationalisations of sectors such as steel. Before Thatcher, however, few believed that natural monopolies such as power and water could sensibly be sold. The policy was originally hit on as a means of ploughing badly-needed investment into the telecoms sector, without running up against strict Treasury rules on capital expenditure – a sort of PFI of its day. But when British Telecom shares were sold at a discount in 1984, the idea developed a momentum of its own, as small subscribers who'd often never bought stocks before scrambled to secure a quick buck. The privatise-and-regulate model went on to be applied to gas, water and – after Thatcher's day – electricity and finally rail. New Labour's acceptance of privatisation is held up as evidence of a "Thatcher consensus", but the new poll suggests that so-called "popular capitalism" is not remembered with any affection today.

The poll tax, or community charge

Graphic: Guardian

Thatcher loathed Labour town halls, which she felt set big budgets because their poor voters would not pay. Rate capping was the early response, but in time she resolved to replace the whole old system of rates on house values with a flat tax on every citizen. Big families got clobbered, while old ladies living alone in big houses cleaned up. At a time when Britain was becoming mindful of the wealth gap that the Thatcher era was producing, the policy ran up against the argument that it was wrong for a duke and a dustman to pay the same. North of the border, the Tories never recovered from trialling the policy on the Scots. Riots followed when it was rolled out in the south. A personal pet project, the tax played a crucial part in Thatcher's downfall. Coalition ministers would do well to be warned that one crucial shortcoming was an inadequate system of rebates that resulted in town halls having to chase poor families for small sums. With effect from this month, their council tax reform will have the same result.

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