Analysis: A towering heavyweight puts our current leaders in the shade

It was, by any measure, the most remarkable career of any woman operating in British politics in the 20th century. That she was the first female prime minister is enough to guarantee her a place in history. But she went far further, and will be remembered as a prime minister whose astonishingly bold reforms fundamentally changed British society. Like it or not, we are all living in her shadow.

That includes the current generation of politicians which followed Thatcher into Westminster. The tributes are flooding in this afternoon. From her allies they are overwhelmingly partisan in their loyalty. From her enemies the studied politeness is excruciating. Ed Miliband and Nick Clegg have praised her radicalism and the boldness with which she remade Britain. There is a lot of attention paid to these tributes because everyone is watching carefully to see if any signs of inappropriate glee emerge. The strength of feeling against her means, whether politically acceptable or not, many will be celebrating tonight.

Thatcher would hate today's government because it is based on compromise. And there is a sense from today's initial reactions that our political leaders know that. Cameron may praise Thatcher for having "saved Britain", but in his actions he is a pragmatist who has worked hard to govern amid all the painful give-and-take negotiations of coalition government.

Today's politics of consensus is as unrecognisable to Thatcher as the state of the country would be in 1990 when she first came to office. She forced Tony Blair to pursue the kind of populism summed up by pollster Philip Gould's mantra "concede and move on". While Thatcher was a politician with the courage to divide Britain, her legacy was to make Labour fight for the centre ground if it wanted to regain power. Blair's decade was based on toothy-smiled accommodations with big business; Thatcher's power was about wrestling with the legacy of the 1970s and jerking Britain out of one way of life and into another's.

Since Blair the shift in the way our leaders conduct their politics has completed its trajectory. The advent of coalition has both created and reflected a new era of broad consensus where the biggest battles are over tweaks to the benefits system and hand-wringing over cuts which all the parties would, more or less, be obliged to implement. It is fitting that Boris Johnson, the only real heavyweight personality of note around right now, has contrasted her memory with "the grey suits of today's politics". Where today's bunch will fade away, he suggested, her memory will linger.

This is the point where sentiment overtakes reality. The equivocations of today's politics are a by-product of a society without really big divides. The gap between the rich and the poor and the enduring suspicion of a ruling elite, the most gaping problems with the UK today, are problems shared by the political parties, not ones which really split them. So voters, struggling to distinguish between the choices offered to them and turned off as a result, return a hung parliament. That leads to a coalition government and a vicious circle begins.

In Thatcher's time the schism was much deeper and fundamentally political. She was of her time – and what marked her out was the extent to which she was prepared to pursue confrontation. Cameron, Miliband and Clegg's views on her are akin to Winston Churchill contemplating the actions of medieval monarchs. They are of different times, of different contexts. There is, simply, no comparison.

Still, politics – not even the death of Britain's most significant 20th century peacetime prime minister – doesn't take place in a vacuum. The death of Thatcher will light a fire under the smouldering local elections contest about to burst into flames across the country. It could even bolster the Tory base in the coming campaign and may intensify frustrations with the necessary deals of the current coalition. Thatcher's death reminds Britain that it was not always like this. Whether or not that is a good thing, of course, depends on your own view of the changes she hammered home in her 11 years in power.