A former head of counter-terrorism has said cuts to police numbers, not the length of sentences, have played the greater role in jeopardising public safety.

Robert Quick, who led Scotland Yard’s counter-terrorism command from 2008-9, rejected claims made by Boris Johnson after last Friday’s attack at London Bridge in which a terrorist killed two people before being shot dead by police.

The prime minister had sought to blame the Labour government, which left power in 2010, for Usman Khan being free. He was jailed over a terrorist plot in 2012 and released in December last year, halfway through his sentence, under tough conditions but without checks as to his suitability.

However, Quick said on Tuesday that the fight against terrorism had been damaged by large reductions made to police funding by the Conservative government since 2010.

“In the 2000s the police worked hard to rebuild neighbourhood policing, with a clear local presence, with staff who were visible and accessible,” he said. “A lot of that has been cut back heavily.

“These are the eyes and ears of the counter-terrorism efforts. It is the foundation stone of security and counter-terrorism and has been broken up in the last 10 years.”

Dedicated counter-terrorism officers escaped the effects of austerity but Quick said this was only part of what was needed to minimise the dangers posed by terrorists to the UK’s defences.

“The counter-terrorism infrastructure has been very relatively left alone by austerity – it’s had to be through necessity.

“The investigative side is good, but once [attackers] are radicalised and cross the Rubicon, the ability to deal with that after arrest and prosecution is very much wanting.

“Counter-terrorism relies on the local intelligence feed from local police divisions. It has been undermined, without doubt, by the reduction of policing presence in communities.

“How we are policing those communities and the connection with communities, seems to have been undermined by austerity.”

Speaking about the effect of sentencing laws on Khan’s attack, Quick said: “It is one case and we do not have enough detail to make sweeping judgments about it. We certainly know a lot about the effects of police cuts.”

The comments were made by Robert Quick, pictured here in 2012. Photograph: Dan Kitwood/Getty Images

On Johnson, he said: “I can’t see much substance in what he says. They are rather tired, almost cliched, remarks that are made in the wake of these tragedies.”

Quick said the Khan case had “called into question” government policy on how to assess prisoners before release, as well as resources in jails.

Khan was on a multi-agency public protection arrangement, which would have involved representatives from police, prison and probation sectors managing him in the community.

The probation sector was separated in 2014 into a public sector organisation managing high-risk criminals and 21 private companies responsible for the supervision of 150,000 low- to medium-risk offenders under a widely derided overhaul spearheaded by the then justice secretary, Chris Grayling.

After years of damning criticism from MPs, inspectorates and former probation officers, the government decided to bring all offender management under the publicly run National Probation Service (NPS) by spring 2021.

The changes took place against a backdrop of 40% real-terms cuts to the Ministry of Justice budget.

Meanwhile the general secretary of the National Association of Probation Officers (Napo), Ian Lawrence, has said that while there was no evidence that the probation service failed to supervise the licence conditions to which Khan was subjected, the issue of community safety could not be divorced from the cuts made to the sector.

“From what we know, [Khan] was given the highest possible supervision plan for someone who has committed that offence,” he said. “Beyond that he would have been given the highest level of supervision that would have involved two or three visits a week with a probation officer.

“On the other hand you can’t divorce the issue of community safety from the reality of what the probation service going through at the moment. While we welcome the movement of 80% of the work back to probation from the private sector, that is going to bring additional pressures.”

He said there were 1,000 vacancies in the NPS, with particularly high rates in the Mids division. “Their staff are facing extraordinarily high workloads. In some cases, 120%, 130% caseloads, and in some cases I’ve heard people having to do two jobs [because they are] helping those on long-term sick.”

He said work was being done to recruit new probation workers but that many new officers did not stay in the job for more than a few months.

“We are working hard with leadership in probation to make the profession more attractive but it comes down to resources … It may be that communication can become disjointed between various agencies – these will come out in a review.”