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Margaret Thatcher was no Eleanor Rigby. For all the apparent emptiness of her final days, the former prime minister is not being buried along with her name.

And today many came. Crowds lined the streets of London as her coffin processed to St Paul's, many applauding as the cortege passed. There were some mild protests but nothing to what the British public in the past has been capable of.

When Lord Castlereagh - the foreign secretary who helped defeat Napoleon and bring peace to Europe at the Congress of Vienna - committed suicide in 1822 by cutting his own throat, his coffin was booed as it was carried into Westminster Abbey.

A contemporary account recorded: "The funeral procession to Westminster Abbey was attended by an immense concourse of people, who, while the coffin was being removed from the late peer's residence to the hearse, and again from the hearse to the Abbey, vented their joy at his death in shouts of exultation."

There was none of that along the Strand, Fleet Street and Ludgate Hill. Instead, a military procession and ceremonial funeral - a state occasion in all but name - to mark the passing of an old lady with dementia who suffered a fatal stroke.

'The hands of historians'

For some, the funeral will draw a line after 10 days of national debate prompted by Lady Thatcher's death, a debate not just about her past but also our future. As the Bishop of London, the Right Reverend Richard Chartres said in his address: "After the storm of a life led in the heat of political controversy, there is a great calm."

Her disciples and detractors will no doubt continue to discuss her legacy but now perhaps from the confines of Conservative dining clubs and the dusty corridors of academia. The great constitutional historian, Peter Hennessy, said: "She now passes into the hands of the historians."

Politicians of all colours will no longer rush to clasp Lady Thatcher to their bosom, each claiming that they are the inheritors of a small piece of her conviction, reinterpreting the myth for their own purposes.

The question of whether or not the funeral was over the top - or even political - is now academic. The complaints about Parliament being recalled for a day of tributes and Prime Minister's Questions being cancelled are over.

The newspapers and broadcasters will find something else to talk about, still puzzled by the polls pointing to Lady Thatcher's continued popularity while their readership and audience numbers hint at less interest in their coverage of her death.

The row over whether a distasteful song about dead witches should be given air time will fade in the memory. Life will move on. One Lib Dem blogger chose the middle of the funeral service to post his musings on "what's going to happen to the Lib Dems in the local elections?".

Continued debate

And yet, is that it? Is it time to draw breath and move on? Well, not quite. There is still the matter of the cost of the funeral that is irking some. The detailed figures will be released in the weeks to come and there will be a row, not just over the cost but also about the way they have been calculated and whether or not the military costs are fully included. There is also the imminent publication of her authorised biography by Charles Moore that promises fresh revelations on well-trodden ground.

But the essential truth is that today's generation of politicians cannot escape the debate about Lady Thatcher's legacy. It is still too soon.

When David Cameron asserts that "we are all Thatcherites now", people will debate his meaning. Is he talking about some new consensus in which the lessons of her premiership should be applied to today? Or is he trying to escape her clutches by sharing the burden of her inheritance, saying she has made her changes and it is time to move on?

Even the Bishop of London had a go at interpreting what she meant when she said "there is no such thing as society". And following Amanda Thatcher's poised bible reading, some are already fantasising about her continuing the political legacy of her grandmother with a lack of shame that might even make a dynastic Gandhi blush.

Conservative MPs will continue, at least for now, to measure their leaders against her benchmark. Voters who supported her will continue to wonder what she would have done to fix today's economic and social ills. And those who voted against her will not forget the lost jobs and devastated communities that followed the decline of their industries during her watch. To cite the inimitable Lord Hennessy again, the legacy of Lady Thatcher will "cling to the velcro of our political life".

The point is not who is right or who is wrong. The point is that the debate about Margaret Thatcher's life and deeds is not over and a funeral and an interment will not bring it to an end. In death as in life the shadow she casts is long.