This is a bit below the thirty years rules but hopefully the mods will be lenient. It is important to understand the context of Thatcher's support for the poll tax. The existing system of rates (a local property tax) was unpopular and regressive as six people in a house paid the same as a single person next door. The local authorities had become centres of opposition to the government and Thatcher wanted to clip their wings.
Conservative party policy had favoured the abolition of rates but had never suggested a poll tax.
Conservatives saw local authority financing as a free rider problem: everyone could vote but only property owners paid rates so there was no incentive for voters to elect low tax (IE Conservative) councils. The Poll Tax was meant to ensure that everyone paid for services, and that councils would have to account to voters for how they spent their taxes. The alternative ways to do this was via a local income tax or sales tax. Thatcher was committed to cutting income tax so that option was out. It was feared that a sales tax would raise inflation.
A subcommittee of Kenneth Baker and William Waldegrave became convinced that a poll tax was the answer . The idea was considered so left field that the Chancellor didn't even attend the meeting where they proposed it because it never occurred to him that they would do something so stupid. Instead they sold it brilliantly. Thatcher saw it as innovative, courageous and a way to destroy her enemies. There was almost no support from the treasury or experts but the nature of government under Thatcher meant they weren't needed.
Originally the tax was to have been phased in but after support for it at the 1987 party conference, Thatcher decided to bring it in in a big bang. This proved even more unpopular.
It is still not clear why Thatcher's usually acute political sense deserted her. The tax benefitted property owners and small businesses and these were close to her heart. By 1990 she was almost completely isolated on the issue.
Sources Anthony King & Ivor Crewe, The blunders of our government John Campbell, Margaret Thatcher the iron lady.
It was conservative party policy. It had been for about 20 years. Thatcher brought it up in 1974 and it was a part of conservative rhetoric through the election of 1987. Basically Thatcher should have been fine implementing what she essentially felt she was elected to do. I can imagine a republican in the US feeling pretty confident after the November elections that their policy is what the people want.
Duncan Townson says this:
A local government tax imposed by the government of Margaret thatcher in 1988–90. The conservative party had long wanted to alter local government finances and get rid of the rates, which charged households according to the value of their property. Thatcher therefore declared that the community charge, a flat‐rate tax to be paid by every adult, would be the flagship of her legislative programme after her victory in the 1987 election. She disliked the rates, as the poor often paid no rates at all yet made the greatest use of the social services. She also thought that the poll tax would make the poor vote more ‘responsibly’ at local elections for low‐spending councils. Under the rating system they could vote for high‐spending (Labour) councils because they did not have to pay for any of the services provided.
emphasis mine
Problem was it turned out to be wildly unpopular in practice. People can often be responsive to calls for 'fairness' in an election without thinking through what the remedies mean for them. Once most people's taxes went up the benefit of the lowered taxes on the wealthy became much less important.
TL;DR it was conservative policy and she was a conservative.
edit boldness fix