Education Secretary Nadhim Zahawi has said parents of children with special educational needs and disability are “tired” of waiting for change and pledged to “get it right with them”.

In the Commons, Labour MP Florence Eshalomi (Vauxhall) said that one constituent with two children with muscular dystrophy had been waiting for 12 weeks for support.

Noting that Mr Zahawi had said parents should engage with the proposals of the Government’s Green Paper on special educational needs and disability, published on Tuesday, she said: “Does the Secretary of State appreciate that they are tired?”

“I don’t think they have the energy to engage in yet another consultation because they are still trying to provide the service for these very children who we want to see flourish,” she added.

Mr Zahawi replied: “She’s absolutely right, parents are tired. My promise to them is that what we’re doing here and the consultation will mean we will get this right, we will get it right with them.”

Liberal Democrat education spokeswoman Munira Wilson said parents have been waiting “three long years” for the welcome Green Paper, adding: “I think people are dismayed – parents, school staff and children alike – that there’s going to be a further 13-week consultation, legislation some time after that when (Mr Zahawi) himself has said this review has been shaped by those parents and teachers.”

Conservative Alicia Kearns (Rutland and Melton) said “too many parents” came to her “broken by the system and they are tired of fighting, particularly going to court”.

Mr Zahawi acknowledged that parents “have fought and feel that they sometimes are let down by the system”.

Education select committee chair Robert Halfon said it had taken too long for parents to be relieved from wading through a “treacle of bureaucracy” to get the right support for their children.

“I know very well what it is like to be a child with special educational needs and having a disability, and I care about this very, very deeply,” he said.

He added: “I welcome that the Secretary of State has taken a grip on this but it is wrong that it has almost taken three years for this Green Paper to come into fruition.

“It is wrong that parents for so long have had to wade through a treacle of unkind bureaucracy, that they have been subject to this awful – as he has acknowledged – this postcode lottery provision, that they wait for months on end to get the ECH plan they should be having and there aren’t enough trained staff.”

The SEND Review, published on Tuesday, outlined a range of proposals to reform how families can access support such as a new single national special educational needs and disabilities (SEND) and alternative provision (AP) system across education, health and care.

The paper proposes for inclusion dashboards to track pupils’ data and drive performance, and a local inclusion plan for each area on how it will meet the needs of pupils.

It says it aims to end to the “postcode lottery” which sees children with additional needs around the country receive varying levels of support.

Also, it says that new national standards should be set across education, health and care to improve performance while education, health and care plans (EHCPs), which help pupils with SEND access support in school, should be digitised.

The paper also says that mainstream schools need to become more inclusive and identify SEND needs earlier to improve support.

The proposals are backed by the equivalent of £70 million in additional funding and the consultation on the plans will be open for 13 weeks.