Institutional racism still plagues policing, a chief constable has warned, as plans were announced to boost diversity in the ranks of officers after pressure from the prime minister.

Chief constable Gareth Wilson, the lead on diversity for the National Police Chiefs Council (NPCC), told the Guardian police forces had been too slow to eliminate prejudice from the workforce and change the way officers treat the communities they serve.

Under new plans unveiled by the NPCC, performance reviews of top officers will be tied to their success in improving diversity. “It is feasible that someone through poor performance will lose their job, of course it is,” Wilson said. But he added that it was unlikely because police chiefs would rise to the challenge.

Wilson linked serious offences such as knife crime to inequalities blighting society, including poor education, housing and life chances, which he said others had to solve.

The diversity plan was announced as fresh figures showed police forces are much whiter than the populations they serve. This is despite promises made almost two decades ago after the Macpherson report into the failings that allowed the racist killers of the black schoolboy Stephen Lawrence escape justice.

Wilson said the police had made progress but that change had been too slow, and that the measures would help make forces look more like Britain.

The NPCC’s diversity plan is part of the effort – announced on Thursday by Theresa May – to stamp out racial inequalities in the public and private sector. It is an issue the PM says she believes in but also plays into efforts by the Conservatives to win more ethnic minority votes to boost their electoral chances.

Policing provides one of the most visible racial fault lines in Britain and the 1999 Macpherson report found police failures were in part due to “institutional racism”. It was a finding police fought at the time and some leaders have claimed no longer applies.

Wilson said: “I think if you look at where we are and what Macpherson said, you could argue that the definition is still true today.”

He added: “We’ve got to recognise we create disparity, sometimes we deal with the consequences of it. There is unconscious bias in the service.

“If somebody belongs to a gang because they have not had the same life chances as others, because of disparities in education, housing or employment, the consequences of that disparity can manifest itself in terms of the people we come into contact with, be that as victims or perpetrators.

“Disparity needs to be dealt with by the whole system and not just one public agency. There is a significant link between inequality and victimisation and people who offend as well. By the time police get involved, there has usually been a failure in the system.”

Official figures show that the racial disparity is now worse for stop and search. According to government figures, between 2010-11 and 2014-15, the likelihood of black people being searched fell from six times that of white people to four times. But in 2016-17 that disproportionality rose again: black people were eight times more likely than white people to be stopped by police, with the vast majority producing no evidence of involvement in crime.

Latest figures show that only 7% of police officers are from a black or minority ethnic (BAME) background, compared to 14% of the population as a whole. Not a single one of the 43 forces in England and Wales has at least the same proportion of BAME staff as the communities they police.

Nowhere is that race gap worse than in the Metropolitan police. London’s 40% BAME population is policed by a 14% BAME police force, leaving the Met thousands of officers short of where it needs to be.

Wilson said: “There could be damage to our legitimacy if we fail to address it now, and that is a consequence of slow progress … There is a significant way to go.”

Wilson said staff support associations for black, disabled and LGBT officers are sceptical about whether the new plans will work. “There is great concern among support staff networks that nothing will change,” he said.

“If this does not change things and we do not get that momentum behind the strategy, I believe our staff support networks will lose all faith in us.”

Her Majesty’s Inspectorate of Constabulary, Fire and Rescue will be asked by Wilson to inspect forces’ progress annually and to name and shame those falling short.

Police chiefs have decided against pressing the government for a change in the law to allow positive discrimination, such as measures carried out in Northern Ireland to boost Catholic recruitment to police ranks .

Wilson said police could do a lot more with existing positive action measures and the government had made it clear it would not countenance a law change.