The wave of knife crime may be linked directly to the police budget cuts instigated by the coalition government and continued under Theresa May, a former head of Scotland Yard has suggested.

Speaking to the Observer after a week in which five people were stabbed to death in London, Lord Blair said the fact that violent crime had risen alongside a reduction in police funding may not be a coincidence. In 2010, when the Conservatives came to power with the Liberal Democrats and began cutting spending, the capital had 4.1 officers per 1,000 Londoners, but by 2016-17 the ratio had dropped to 3.3 officers per 1,000, according to figures from city hall.

The total number of offences involving a knife or bladed instrument recorded by the Metropolitan police in the year to March 2018 rose to 40,147, a seven-year record.

Blair said: “Crime is clearly an indicator of societal health, particularly violent crime. We know that crime just about peaked in 1993 and went on going down until something like 2010 to 2012, and then started to go back up again.

“One of the things that a statistician always looks for is to see whether a change in behaviour is a coincidence or whether there is causation. It does seem odd that the cut in budget for policing by 20% coincides with a significant rise in crimes of all sorts. Is it coincidence or is it causation?”

His comments follow warnings by MPs last week that police cuts may have “dire consequences for public safety”. Trust in the police, said a report by the public accounts committee, is “breaking down” as forces struggle to respond to crime because of government cuts.

Amber Rudd, a former home secretary, angered senior officers by claiming that police cuts were not to blame for the surge in knife crime.

Blair, who as Met commissioner between 2005 and 2008 tried to find “lasting solutions” to youth violence, also warned that the positive impact of neighbourhood policing was “probably fading under the pressure of finance”.

More broadly, he warned that the threat of an emerging far right and its divisive discourse should be viewed extremely seriously.

“At the end of my period of office the far right had done what the far right always does, which is break up into lots and lots [of factions].

Jay Hughes, 15, was one of five people stabbed to death in six days in London. Photograph: Dan Kitwood/Getty Images

“But what we have now is a nastiness with the English Defence League and so on. Which I imagine is of deep significance to those who are concerned about the integrity of the British state,” said the crossbench peer.

Blair is chair of trustees at the Woolf Institute, which is affiliated to Cambridge University and aims to encourage tolerance between people of different beliefs. He said that the institute planned to carry out research into the effects on British society of this increasing polarisation.

Among other initiatives the institute, which has just celebrated its 20th anniversary, is building a “UK inclusivity index” to measure and map levels of intolerance in different parts of Britain. “It will be what we can do to assist people to understand what polarisation means, what inclusivity means,” said Blair.

Blair, who became the country’s most senior police officer shortly before the terrorist attacks on London on 7 July 2005, said the bombings – which killed 52 people and wounded more than 700 – had led him on a personal journey into faith and “religious identity” that began with attempting to understand what motivated the four suicide bombers.

However, he said that elements of the media had prevented a proper debate concerning Islam and its true meaning. “Some of the coverage of Islamic matters has been appalling, look at some of the fuss about sharia law,” he said.

On an international scale, Blair said those who dismissed the role of religion in global affairs needed to have a rethink.

“We have to accept that the idea that religion is no longer important is completely deniable at the beginning of the 21st century. Religion is one of the key flashpoints that we have, and events that happen in Syria as we know play out on the streets of London or elsewhere.”