The “outrageous discrimination” in the treatment of mental health illness in the NHS will be ended by the setting of a new two-week waiting time target for people who suffer a first episode of psychosis, Nick Clegg will announce on Tuesday.

In his speech to the Liberal Democrat conference, the deputy prime minister will announce plans to ensure that the treatment of mental health conditions is placed on a level with physical health from 2015. He also aims to force a public debate to challenge the taboos around mental illnesses.

Norman Lamb, the Lib Dem social care minister, said the changes, which will also set new waiting time targets for those afflicted by common mental illnesses such as depression and anxiety, are designed to tackle the “totally haphazard” treatment of mental health.

Lamb told BBC Breakfast: “It ends the really outrageous discrimination against mental health. If you have suspected cancer you get seen by a specialist within two weeks and you start your treatment within a month of diagnosis – and rightly so. But if you have a mental health problem, if you experience a first episode of psychosis, for example, it is totally haphazard. So when the last Labour government introduced access and waiting time standards – and they were right to do so – they left out mental health. That discrimination has to end.”

In his speech, Clegg will say three-quarters of patients needing “talking therapies” for conditions such as depression will be guaranteed treatment in six weeks, with 95% starting treatment after a maximum wait of 18 weeks.

Patients with more serious problems such as psychosis will be offered treatment within two weeks of referral, bringing the service in line with targets for cancer referrals. The aim is to ensure the targets are being reached by 2020. The programme will have to be phased, so by 2016 the aim is for at least 50% of people experiencing a first episode of psychosis not to have to wait longer than two weeks.

Mental health campaigners welcomed the promise as a significant advance.

The coalition announcement, agreed with the Conservatives, is backed by £120m of extra funding over the next two years, with £40m this year and a further £80m in 2015-16.

Just over £30m of the funding will be earmarked for early intervention services for psychosis and crisis care.

It is highly unusual for a party leader to put treatment of mental illness at the centre of a mainstream party policy programme, let alone at the heart of his annual speech to his party conference.

Clegg will say: “It is wrong that relatives and friends needing a hip operation can expect treatment within a clear timeframe but someone with a debilitating mental health condition has no clarity about when they will get help.

“I want this to be a country where a young dad chatting at school gates will feel as comfortable discussing anxiety, stress, depression, as the mum who is explaining she sprained her ankle.”

Clegg will tell his conference: “Labour introduced waiting times in physical health – we will do the same for the many people struggling with conditions you often cannot see that we often don’t talk about, but which are just as serious.”

Saying compassion for those suffering mental illness is a great liberal cause, he will promise to make mental health one of his party’s top priorities in its manifesto, setting aside as much as £500m more in a long-term programme.