My taxi was about 90 seconds behind the murderers who struck on London Bridge last week. My wife and I saw their victims on the road. It made no sense until we stopped and got out. Then with horror we realised what we were witnessing.

As everyone has already said, the emergency services’ response was flawless. A police 4×4 screeched up behind and two officers jumped out with submachine-guns. Within minutes, we learnt afterwards, the jihadis had been shot dead — but only after they had killed eight people, and injured scores more.

Hundreds of others will have been on that bridge or in Borough Market. I suspect all of us will be thanking the police, but also wondering how it came to this. Britain has been hit three times in three months: a sign, surely, of a lapse in our defences. And not by mystery killers either. One, Khuram Butt, had featured in a Channel 4 documentary called The Jihadis Next Door, and another was on a European terror watch-list. No wonder so many are saying that the British government has failed in its most basic duty: to keep people safe.

Theresa May said that the nature of the threat is becoming ‘more complex’ and ‘more hidden’. This doesn’t ring true. The attack on London Bridge wasn’t planned by a sophisticated network, but by thugs armed with hire cars and knives. Khuram Butt was filmed kneeling reverently in front of a black Islamist flag — not at some secret jihadi gathering, but in Regent’s Park.

Just in case MI5 weren’t watching the Channel 4 documentary, Butt was reported to the authorities by the Quilliam Foundation, who released an indignant press release after his killing spree. In a violent scuffle at a public event in July last year, it said, he had branded their researcher, Dr Usama Hasan, an ‘apostate’ who took ‘government money to spy on Muslims’. Quilliam were told airily that he was already ‘known to intelligence’. Butt was arrested and given a caution.

Another of the attackers, Youssef Zaghba, a Moroccan-born Italian, was branded a terror suspect before he’d set foot in Britain. In March last year, he had been stopped by the Italians while heading to Syria — and lest there was any doubt about his intentions, he told officials at Bologna airport that he was ‘going to be a terrorist’. A promise that he fulfilled on British soil last Saturday. Why was he let in to Britain at Stansted airport even though, according to Italian officials, we ran checks on him? Inevitably, the Home Office refused to comment on this.

Until recently, we had great confidence in the abilities of Britain’s police and intelligence agencies. We were better at stopping terrorists, the evidence suggested, than our European neighbours — especially the French and Belgians. That confidence has now been shattered. Amber Rudd, the Home Secretary, said: ‘These past three months mean we’ve entered a different phase, which is why we need to do something differently.’ But do what?

The answer certainly doesn’t lie in more armed police. Karen Bradley, the hapless Culture Secretary, was grilled about government cuts to police firearms units since 2010 — but believe me: there were so many of them on the bridge that they could have taken on an army. Nor do I think deporting foreign jihadis will solve the problem on its own: many attackers are British-born, or have British passports.

The problem is the numbers. MI5 needs to watch 3,000 people regarded as being in ‘active sympathy’ with Islamist terrorism. The security service would have to be about 50 times bigger to keep full tabs on all of them. Limited resources force ‘very tough prioritisation’ and a categorising of threats, says a well-placed source. Watching the likes of Khuram Butt could mean pulling agents off more obviously dangerous cases — the top-category Islamist ‘P1As’, for instance, who MI5 are certain are ‘going to kill someone’ unless they are stopped.

Throwing cash at the problem — as Jeremy Corbyn and Tim Farron, two late converts to the cause of defending the realm, have pledged to do — would help only up to a point. More resources would reduce the risk but, I’m told, only in the way that ‘playing roulette with three balls instead of one increases your chances of winning’.

That’s not to say nothing can be done. Prison sentences for convicted jihadis could be longer, as Theresa May this week indicated may happen. Anjem Choudary, the radical preacher whose henchmen have been involved in so many plots, was jailed for just five and a half years last year for encouraging support of Isis.

When I briefly worked at the Ministry of Justice last year, I saw where he was imprisoned, and who his fellow inmates were: he is locked up alongside some of the most reviled criminals ever to pass through English courts. But while many of them will (rightly) be behind bars until their dying day, Choudary will be out in five years — maybe sooner if he behaves himself. Butt, it appears, didn’t get radicalised online: it was partly Choudary’s influence in person. And soon Choudary will be out, pouring poison into young ears again.

There is also a psychological aspect to the spate of recent attacks. Islamists used to fear that their planned attacks would be thwarted, but recently they have realised — rather like the rest of the public — that Britain’s security system is fallible. We saw this, too, in the wake of 7/7, with the failed copycat suicide attack that followed weeks later.

The British response has been inadequate. It’s not illegal to be a jihadi sympathiser, but there are things that can be done about the jihadi next door. We used to have control orders, which were abolished under David Cameron in favour of ‘Tpims’ (Terrorism Prevention and Investigation Measures), which are resented by the security services as being time-consuming, bureaucratic, and ineffective. Tpims oblige a suspect to live at home and stay there overnight: that wouldn’t have prevented the London Bridge atrocity.

Ultimately, though, dealing with these terrorist suspects once they are radicalised is like a surgeon dealing with cancer. You can cut out the disease when it appears, but it’s better to deal with the root causes — to prevent radicalisation, particularly among young men.

The Prime Minister has said that ‘enough is enough’ and that she is serious about uprooting terrorism. But how serious? We will soon find out.