Amy Winehouse's father, Mitch, is meeting the Home Office minister James Brokenshire to discuss plans to set up a drug rehabilitation centre in his daughter's name.

Winehouse is being joined by his daughter's managers, Raye Cosbert and Trenton Harrison-Lee, and Sarah Graham, a former cocaine user and addiction expert, to highlight a gap in residential treatment services for young people who cannot afford private treatment.

A family spokesman said Mitch Winehouse felt strongly about the fact that addicts can face a wait of up to two years for NHS treatment. "He realised that if the family didn't have money for Priory-style treatment it would be difficult to get help," the spokesman said.

Graham said: "We didn't know it [Amy's death] was going to happen but we hope it will show people that addiction is something that can kill people when they are very young and that we should not wait until it is too late."

She said most treatment was not residential but accessed in the community. "Rehabilitation is more expensive than treatment in the community but in reality most desperate young people cannot access it," she said. "It might be because their dealer meets them at the school gates or it could be that they are getting abused at home."

Mitch Winehouse met Graham when they both gave evidence to the Commons home affairs committee in October 2009. Graham said Britain's only NHS rehabilitation centre for young people – at Middlegate in Nettleton, Lincolnshire – closed last year.

Winehouse said in his eulogy at his daughter's funeral last week that Amy had just completed three weeks of abstinence and may have struggled to deal with the sudden withdrawal. A postmortem examination proved inconclusive and an inquest was opened and adjourned with no cause of death given.

Keith Vaz, chairman of the Commons home affairs committee, who also met Winehouse on Monday, said: "I strongly support Mitch Winehouse's initiative in trying to improve residential rehabilitation services for young people as well as found a centre for the performing arts.

"When he gave evidence to the home affairs select committee inquiry into drugs two years ago, he was very clear that drug treatment in the UK was hard to access and long waits were common, and we have already expressed our concern at reports that residential rehabilitation is not readily available.

"Despite his obvious grief following the death of Amy, Mitch Winehouse has decided to pursue this important campaign to help rehabilitate those most vulnerable in our society."

Paul Hayes, chief executive of the National Treatment Agency, has said the popular image of luxury rehab, beloved of celebrities and the tabloids, is not representative of the mainstream treatment and recovery services provided in Britain by the NHS and charities.

"These services are widely available and for some years now official statistics have confirmed that more than nine out of 10 patients wait less than three weeks for treatment in England. There is an ongoing challenge for the system to respond flexibly to patient choice and ensure that people with drug problems are helped to become free of addiction in the most clinically appropriate way as quickly as they might wish," said Hayes.

He insisted there was a clear trend towards fewer young people needing treatment. But Simon Antrobus, of the treatment provider Addaction, said his organisation's ability to provide support was at risk as funding for some community-based services had been cut by as much as 50%.

"While it is good to see that fewer young people are using drugs and alcohol, we cannot become complacent. We need to ensure that specialist support remains available for everyone who encounters problems, whether it is the person themselves or the family around them," Antrobus said.