Terrorism doesn’t work. It takes the lives of the innocent, but strengthens the resolve of the survivors. Yesterday’s attack on the Houses of Parliament could have been very much worse, but even if it had been, it would not have made opinion move one iota towards the terrorists’ point of view.

Most of us will have seen pictures of Churchill standing in May 1941 amid the bombed out ruins of the House of Commons. He said it must be rebuilt just as it was before, and that is what happened.

“It’s like the war,” a lady in her eighties remarked to me this morning. “You can’t give in to people.”

And that was the mood yesterday afternoon and evening at Westminster. The attack made people value what we have even more, in particular the work of the police, who run such dangers in the line of duty.

In Westminster Hall, where many hundreds of us – MPs, peers, administrators, researchers, cooks, visitors, journalists – found ourselves confined for some hours, there was a deep sense of shock at the killing which had happened just outside, in New Palace Yard.

But there was also a willingness to be amused: a determination, not to make light of what had occurred, but to respond with a kind of jauntiness rather than with unrelieved gloom.

A veteran of the troubles in Northern Ireland, to whom I remarked that he must be more used to this kind of thing than most of us were, responded in a dry tone: “Oh no, we never kept people hanging around like this.”

An MP who soon after the attack, had entered the Tea Room in search of sustenance, related that he found it deserted, and had resisted the temptation to finish a still warm cup of coffee, and to steal a chocolate bar.

Ordinary life went on. There was ordinary speculation about whether there will be an early general election. A Lib Dem made some ordinary claims about how amazingly well they are doing in the West Country.

The atmosphere became a bit like a cocktail party without the drinks, though staff were handing round water to those who wanted it. Beneath the greatest medieval roof in Europe, a hubbub of conversation swelled, until at about 7.30 p.m. we were released en masse up the steps at the St Stephens end of the hall, and were free to return to our offices if that was what we wished to do.

About an hour later, as I cycled out of the House of Lords end of the building, a police officer asked me if I had been a witness to the attack. There was about him and his colleagues an air of relaxed efficiency which was very reassuring.

Every day that I come to Westminster, I cycle into New Palace Yard, exchanging a word or two of thanks with the officers on the gate. Yesterday, perhaps 20 seconds after the attack, I saw from a press gallery window a lone cyclist ride in by the usual entrance – the exit being where two bodies already lay on the ground.

Officers must have shouted to him to take cover, which he did with impressive speed, in the black hut where the police monitor new arrivals, and from which they control the blocker which would prevent a vehicle getting very far into the yard. This, it later emerged, was Jo Johnson MP, arriving for a vote.

Let us go on having a democracy where MPs can arrive by bike for a vote.