Official reviews will clear MI5 and the police of making serious mistakes that allowed terrorists to strike Britain in four attacks this year, the Guardian has learned.

But the reviews will also make a series of recommendations to minimise the chances of missing future attackers, including a new computer algorithm to detect behaviour that could indicate involvement in terrorism.

The internal inquiries were set up in the wake of the atrocities and have been carried out by MI5 and the police themselves, overseen by a barrister.

The reviews have found information was received by MI5 about the Manchester attacker, Salman Abedi, which could have been given a higher priority. But that conclusion is reached with the benefit of hindsight, sources say, and nothing in the reviews demonstrates that clear chances were missed to stop any of the attacks that killed 36 people.

Some may see the notion of MI5 and the police investigating themselves as unsatisfactory; parliament’s intelligence and security committee (ISC) has been unable to investigate because the prime minister failed, until last week, to establish it after the May 2017 election.

The ISC will meet on Tuesday and will consider if it should hold its own inquiry into the attacks in London and Manchester.

The report concerns attacks in Westminster, Manchester, London Bridge and Finsbury Park.

The reviews into the four atrocities between March and June where terrorists beat Britain’s defences were overseen by a barrister, to provide assurance to the government that the inquiries were thorough.

No individuals are criticised in the reports, and that includes MI5 director-general Andrew Parker. Some media reports had claimed the inquiries into the attack would be so damning that his job might be in jeopardy.

Among a series of recommendations are improvements in:

• Intelligence handling.

• The collaboration between MI5, which leads on counter-terrorism intelligence, and the police, which carries out enforcement action such as the detention of suspects.

• How closely the two organisations work together.

• The handling and potentially increased sharing of data with other parties, to put in place better preventive measures.

This is understood to mean better use of data analytics to go through the digital life of current and former suspects, on their smartphones and other devices, for clues indicating they may be more involved in terrorism than previously thought.

Security officials will develop a new algorithm to scour the list of 20,000 former suspects, who are classed as posing little danger, to spot signs they may be re-engaging in terrorism, and then alert intelligence officers.

Those on the list of former suspects currently have little or no resources spent on them.

It is claimed that Khalid Masood, who attacked Westminster in March, Salman Abedi, who bombed Manchester in the May, and Khuram Butt, who attacked London Bridge in June, had previously come to the attention of counter-terrorism officials. The two terrorists who murdered Lee Rigby in 2013 were also in the pool of former “subjects of interest”. Britain’s counter-terrorism system currently actively investigates 3,000 people.

The new algorithm is hoped to lessen the chance anything will be missed. It will inform decisions made by human case officers and analysts, not replace them.

The independent monitoring of the police and MI5 reviews has been carried out by David Anderson, the former independent reviewer of counter-terrorism legislation. One security source said his role was to make sure that MI5 and the police counter-terrorism network “were not marking their own homework”.

Anderson’s “assurance” role followed a request by the government’s National Security Council. He submitted his report to the home secretary on 2 November, and a public version is expected to be released in the last week of this month or in early December.

MI5 and the police counter-terrorism network carried out two internal inquiries. Each organisation carried out a post-attack review to see if errors were made, whether different decisions could have been taken, and how the available intelligence was handled.

The second part looked at how to improve their operations, especially given the view among counter-terrorism officials that the level of attack plotting and supporting activity is at an all-time high, the result of a shift, not a temporary spike.

The ISC is expected to receive both Anderson’s public and private report.

While the part of the reviews assessing if counter-terrorism officials made mistakes may attract more attention, the bigger focus among MI5, police and government is on retooling Britain’s efforts to cope with an increased threat from potential violent jihadists and a growing extreme rightwing terrorist threat.

Police are trying to reverse a 7% cut in funding they get from the government to catch terrorists, while money has already been earmarked for MI5 to grow its staff by 25% to reach 5,000 people.

Those decisions were made before this year’s attacks and before analysts assessed the terrorist threat had reached a new level of seriousness.

The reviews make no demands for controversial new laws or to shift the balance between human rights and security. There are no findings for a return of the stronger control orders which were scrapped by the Conservative-led coalition government and replaced by the terrorism prevention and investigation measures, seen by some in counter-terrorism as weaker and sucking up resources.

Nor are there any findings supporting an extension to pre-charge detention. Sources say police and MI5 accept that the UK already has a strong set of laws after decades first combating Irish republican and then Islamist terrorism.

Police have said they want longer sentences for those involved in terrorist propaganda, amid predictions that Islamic State will increasingly spread its message virtually, as it loses territory.

It is not known if the MI5 and police reviews into the attacks or their recommendations to boost their efforts will be published in any form, though some of their findings may be guessable from the public version of Anderson’s report.

The attack at Parsons Green tube station in September is not part of these reviews.

New figures showed investigators have taken 300,000 items of terrorist propaganda off the internet since 2010, but the rate is slowing down, in part because technology companies have stepped up their efforts after years of pleading by the government, law enforcement and security service.