In 18 years as a journalist, I have seen how hideous tragedies can lead to disastrous decisions, from the Dangerous Dogs Act right up to the war on terror. Everyone panics. The impulse is to do something, anything, even if it is the wrong thing.

As six cyclists are killed in the capital in 13 days, everyone at City Hall is as horrified as any other Londoner. But if we have a duty at times like this, it is to think straight – and to talk straight, not to promise things we can't or shouldn't do.

Not everyone has been thinking straight. The former transport secretary, Lord Adonis, has called for urgent action – but then, literally in the same breath, demanded a full independent review, something that would delay any action by months.

We've already had a review. We're acting urgently, upgrading all our existing superhighways with fully and semi-segregated cycle lanes. We're doing new segregated tracks, new backstreet quiet routes, remodelling dozens of junctions and spending almost £1bn. Nothing is closer to the mayor's heart than this.

What, I've asked many cycle activists, what is it you want us to do that we're not doing already? The usual answer is "do it quicker". But we can't simply slap in panic changes that might make cyclists safer at the expense of other people's safety. And if we're reducing roads' traffic capacity, as we are, we need changes over a far wider area to reduce vehicle numbers coming in to those roads. Our plans are the biggest change to inner London's road network in perhaps 30 years. That is why we cannot, and will not, promise to do this overnight.

The other big call is for a morning rush-hour lorry ban. We're not against it, and we're studying it – but the case is finely balanced. Two of this year's 14 deaths in London could have been prevented by such a ban (the other 12 happened outside the rush hour, or did not involve lorries.)

But a ban could have a big impact on the economy – particularly construction, which would lose a quarter of its winter daylight – and on Londoners' sleep and health, as lorries unable to move in the mornings start delivering at night.

It is claimed that Paris's lorry ban helped it remain free of cyclist deaths in 2012. Untrue: greater Paris had 17 cyclist deaths last year. Central Paris, equivalent to our Zone 1, had five – four more than central London.

I understand the media furore. I know the people behind it are mostly allies who want what I want. But I worry that they are unwittingly causing great collateral damage to the very thing, cycling itself, that we want to promote. Right now, the message to any would-be cyclist is that you shouldn't; that the roads are unsafe; and that nothing is being done about it. The word "carnage" is used. But none of these things is true either.

In 2002, London had 110 million cycle trips, of which 20 ended in death. By last year, there were 180 million trips and 14 deaths – a reduction per trip of more than half. That is not "carnage". Serious injury rates are the same as they were 10 years ago.

I fear the furore is aiding those who say we shouldn't encourage cycling. I'm afraid it's scaring cyclists away. And I'm worried that in trying to help cyclists City Hall is treated as if it has nationalised every accident; that we are held responsible for every death and injury on the roads, however caused. That won't deter Boris Johnson – but future politicians may conclude it would be easier to avoid the subject.

I'm not saying we should stop talking about safety. But we should be more careful how we discuss it – and in particular, about the conclusions we draw from tragic, but rare, events. The blunt fact is that cyclist deaths tell us relatively little. There are too few of them. In the first half of 2013, only three cyclists died in London – one every two months. In the recent spate, it was every two days. Are these same streets 30 times more dangerous than just a few months ago?

The facts of each death are different. We should not make assumptions before we know those facts. We should particularly not assume, as so many have, that the latest fatalities were the fault of the road design. Indeed, two of the three deaths described as happening "on superhighway 2" actually took place only in its general vicinity. The victims were not using it when they died.

We badly need better routes and safer roads. But even the world's best cycling infrastructure doesn't immunise you against harm. Even that nirvana called Amsterdam averages six deaths a year, in a city with about the same number of bike trips as London (Amsterdamers cycle more often, but there are fewer of them).

The chief executive of the London Cycling Campaign wrote last week: "We want to know when the dying will stop." Well, we can, and we do, promise to improve safety. But we cannot, and do not, promise to eliminate cyclist deaths. If that is the test the cycling lobby sets us, we, and every large city on Earth, will fail. That is another reason not to turn each individual tragedy into a national emergency.