Most of the hundreds of thousands of people who attended this weekend's protests against public spending cuts expressed their anger at the Government in the traditional way: with drums and whistles, slogans painted on home-made placards and thousands of voices all chanting the same words: no more cuts.

Out on the edges of this peaceful crowd, however, was a much smaller group who seemed determined to cause mischief: missiles were thrown, police officers were hurt and more than 200 people were arrested.

Perhaps, inevitably, it is the missiles that have attracted more attention than the placards, but the 400,000 people who took to the streets of London this weekend did so for a good reason – and we shouldn't forget that because of the behaviour of a tiny minority.

Yesterday, as the damage and debris was being cleared from the streets, the behaviour of this small minority was – quite rightly – being condemned by business leaders, politicians and the organisers of the protests themselves. But it should be remembered that the damage was caused by a few hundred rogue elements at the fag end of a day of protest; for most of the day, thousands of people got their message across peacefully and publicly – as they have the right to do.

The best way to understand what the protests were really about is to look at the people who were there: teachers, nurses, firemen, council workers, NHS staff, the retired; the very groups, in other words, who will feel the slash and cut of Chancellor George Osbourne's knife the worst. Many of these people have never marched before but they have been driven to by the most savage cuts in public spending since the 1930s. A few days ago, the Chancellor had an opportunity to do something about that in his Budget; instead, he did nothing to prevent hundreds of thousands of public sector workers losing their jobs in the coming months. It is any surprise that many of them were in London trying to prevent that happening?

We know, because the TUC has said so, that this weekend's action was planned to be the first of many over the coming months and it's crucial that politicians support the right for such protests to go ahead and do not overreact to the violence at the weekend. The Education Secretary Michael Gove warned Labour leader Ed Miliband not to attend Saturday's event because there was a risk, he said, that a family event could move into something darker, but that would be an argument against any form of protest. It was right that Mr Miliband was there, just as it was right that he condemned the protesters who went too far.

As well as the Labour leader, the police have also emerged from this well as it seems that they have learned some lessons from previous mistakes and have softened their approach to handling large protests. The so-called kettling technique of confining protesters to one small area was used at the base of Nelson's Column on Saturday, but in other respects the police were clearly attempting a different approach, even keeping in touch with the protesters by twitter – and that is welcome.

However good the policing becomes though, it is inevitable that events of this scale will attract a small amount of trouble. This was the largest public protest since the marches against the Iraq War in 2003 and one of the biggest demonstrations in British political history. There were arrests and there was damage but there was something far healthier and better on view too: the right to protest and the duty of the State to ensure that we can do it. The recklessness of a few hundred should not distract from the anger and frustration of hundreds of thousands.