At least one of the attackers on the 7/7 London Tube bombings was known to the intelligence services. 
Khalid Masood who attacked Parliament on March 2017, killing several people, was known to the intelligence services. 
Salman Abedi who blew himself up – killing 23 at a concert in May 2017 was known to the intelligence services. 
At least one of the attackers in the June 2017 London Bridge attack appears to have been known to the intelligence services. 
In at least some of the cases above (Abedi and one of the as yet unnamed London Bridge attackers) there are claims of multiple reports by the public to the police and even the Prevent helpline (set up to allow the public to report concerns about terrorists).
In fact this pattern is repeated for virtually all (if not all) the recent terrorist attacks in Europe including the French theatre bombings (November 2015) and the Madrid train bombings (March 2004).
This fact – that all these criminals are already on the watch lists of the intelligence agencies – shows what amazing work the intelligence services do.
However; this fact raises the question as to whether or not these attacks could have been prevented. After the Manchester attack MI5 leaked to the press that at any one time they have 23,000 in a wider pool of suspects and 3,000 under active scrutiny. They only have resources to keep 3,000 under active surveillance at any one time.  It would appear that in the 4 cases above of attacks on UK soil the attacker(s) known to MI5 were in the 23,000 list but not in the 3,000 list.  Given that none of the above 4 attacks in the UK were carried out by people in the 3,000 list we can reasonably infer that this level of surveillance may be effective in preventing attacks. The conclusion is obvious; at the least MI5 should be resourced to place all 23,000 under active surveillance. Given the levels of training presumably required for this kind of work this cannot probably be done overnight; but it seems to be a direction worth heading in.
Beyond that there is the fraught and extremely problematic question about the existence in the UK of thousands of people who are basically potential terrorists. Surveillance is extremely resource intensive and can only go so far.
At the same time; it is time perhaps to drop some of the niceness and absurdities that this is not to do with Islam. All of the attackers above thought that they were doing something in the name of Allah and most seem to have thought that they were acting for the benefit of Muslims suffering under Western bombs in the Middle East. (The 7/7 attackers gave this as their reason. Masood did). That alone means that this is a problem not just with ‘extremism’ but with Islamic extremism. The UK is, again a fact, involved in an illegal military intervention in Syria and illegally invaded Iraq in 2003. That Muslims are suffering considerably in the Middle East is incontrovertible. Even if the individuals who commit these atrocities are psychologically damaged people acting out of their own personal problems who have just latched onto a cause to make themselves appear heroes it remains the case that there is an undoubted connection to what is happening in the Middle East. Chaos in the Middle East leads to chaos at home.
The argument that ISIS ‘hate our values’ and would attack us even if we withdrew from the Middle East is not serious. ISIS always overstate the case; it is part of their modus operandi. Furthermore; whatever some Twitter account linked to ISIS says the fact is that it is the sight of Muslims suffering in Iraq, Syria and Libya which gets some British Muslims so worked up. The argument that there is no connection is simply imperialism; an attempt to continue our war ad infinitum by claiming that all the aggression is on their side. In this link Labour politician Andy Burnham gives a very good illustration of the kind of sheer phantasy land that deniers of the connection between British Foreign Policy and domestic terrorism exist in. He claims that “let’s remember that the appalling atrocity of 9/11 happened before interventions anywhere”. This is completely untrue. 9/11 was carried out by a group which had been part of a movement funded by the CIA in Afghanistan to fight the Soviets. Bin Laden gave as his rationale the Western presence in Saudi Arabia. Andy Burnham shows precisely the kind of childish thinking which would, if allowed to inform policy, ensure we will never escape from this problem. These people don’t drop down from outer space. Their actions – even if they are the actions of a deluded minority with psychological problems – are connected with British interventions abroad.
Britain has a clear track record of interventions in the Middle East which create chaos and cause suffering to Muslims. There are 2.75 millions Muslims living in the UK. Of these 4% “sympathise” with suicide bombings.  That makes 110,000. Of these 1% “completely sympathise” – which is 27,000. MI5 says that 23,000 are ‘subjects of interest’. Just 3,000 are being actively watched at any one time. There is a real problem here. One which the political class is dancing around the edges of. Either because, on the one hand, they don’t want to admit the connection between these attacks and Britain’s involvement in ill-thought out interventions abroad (which they want to continue) or because they are too wedded to a politics of ‘promoting diversity’ at all costs and can’t bring themselves to admit that there is a cultural and religious dimension to this.
There is a serious lack of real politik here. As long as this is the case this spiral will continue.
Update 6 June
In a truly disgusting spectacle of political blame avoidance we can now see Foreign Secretary Boris Johnson and London Mayor Sadiq Khan trying to blame the police for letting these events take place. It should be evident to anyone that surveillance alone cannot stop 100% of these attacks. There are thousands of people in this country who are potential terrorists. MI5 can play a guessing game about which ones are likely to move to the active stage but it is inevitable that they can’t always get this right. Human behaviour is not 100% predictable. The clear reality here is that this is a political problem; here we see two political class politicians trying to duck the problem by making wholly impossible demands on the police.
6. According to this article in the Guardian one of the London Bridge attackers was in the 3000 list. However a) no source is given and b) the police had said he was no longer considered a threat which would suggest he was not being actively monitored. RT who also provide a quote but without giving many details about the source say that Butt, one of the main London Bridge attackers, was classified as “low priority” which would appear to mean he was on the 23,000 list and not the 3,000. All matters considered RT is probably right.