Firstly, you have to remember that the media, then and now, loved her. They were largely based in London and the city of London did very well because her privatisation of everything in sight made the City (financial sector) a lot of money.
Secondly, she was elected during the epic Winter of Discontent, when an overreaching by the unions had resulted in a backlash of hard-right feeling.
Thirdly, she was extraordinarily lucky to have an opposition that was determined to self-destruct. The Labour party was falling apart in the Eighties and in no shape to actively oppose her. They fell out with the unions, which cut off most of their funding, so they had no cash to fight elections; elected as their leader a man who, with the best will in the world, was too easily distracted and too prone to windbaggery to effectively oppose her. Labour wouldn't really recover until the mid-Ninties when they took a hard swing to the right under Blair and effectively ran as Tory-lite. The Liberal and SDP parties were characterised during this period by fratricidal in-fighting.
Fourth, she promised the earth and the media covered for her when she failed to deliver (the power of the media in this country really can't be overstated). The people who did well out of Thatcher's reign were the same people who had the ear of the media.
Fifth, the British Constitution means that we don't vote for Prime Ministers, we vote for parties and the head of the winning party becomes PM. While a huge amount of people loathed Thatcher, most people liked their local MP and voted for them. That meant that the Tories got a majority in Parliament and Thatcher became PM even though many people disliked her as a person.
Six, this was during the same time as Reagan was effectively telling America that greed is good, the same period when much of the world was trending to the right. We thought this was how things were done.
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