Theresa May has admitted that homelessness is a source of “national shame” in a major speech where she vowed to make it her personal mission to tackle the housing crisis.

After a week dominated by Brexit, the Prime Minister returned to her domestic agenda by committing to stamp out rough sleeping entirely within a decade, through giving more money to town halls and boosting spending on mental health and addiction support.

Announcing a shake-up of planning rules, Ms May said the “crisis of unaffordability” in housing was enforcing deep social inequality between people of different generations and different economic backgrounds, while making social mobility almost impossible.

It comes after a homeless man died just yards from the entrance of the Palace of Westminster, prompting national outrage as the numbers of rough sleepers in England soared to record levels.

Speaking at a planning conference in London, Ms May said: “In 2018, in one of the world’s largest, strongest economies, nobody should be without a roof over their head.

“This isn’t just a British problem – in recent years homelessness has risen across Europe – but it is a source of national shame nonetheless.

“That’s why we pledged in our manifesto to halve rough sleeping by 2022 and eliminate it altogether by 2027.”

In a wide-ranging speech, Ms May also took aim at developers who do not build homes quickly enough, saying she would “not rule out any options” to tackle delays in homebuilding, including penalising those who sit on valuable land where they have planning permission.

Expecting private developers to deliver enough homes is “pie in the sky”, and the Government must step in to make sure enough housing is built, she said.

She said young people and first-time buyers were “right to be angry”, as many could not afford to buy a house without financial help from their parents.

Ms May said: “The result is a vicious circle from which most people can only escape with help from the bank of Mum and Dad. If you’re not lucky enough to have such support, the door to home ownership is all too often locked and barred.

“Talking to voters during last year’s election campaign, it was clear that many people, particularly younger people, are angry about this.”

She went on: “But the impact of rising prices goes beyond the simple division between housing haves and have-nots. This crisis of unaffordability is also creating a crisis of almost literal social immobility.”

Ms May also promised action to protect renters from unscrupulous landlords after the “tragedy of Grenfell Tower shone a spotlight on experiences shared by many tenants”.

She said: “Whether you are renting by choice or necessity, you’re not any less of a person for doing so and should not be treated as such.”

The Prime Minister also set out plans for extra protections for the green belt, calling for an increased density of homes within urban areas to meet demand.

Senior Tories, including former housing minister Nick Boles, and the Conservative head of the Local Government Association warned ahead of the speech that “the nonsense will go on and nothing will change” unless the proposals were strengthened.

Their concern was echoed by Labour, who said the plans were too feeble to tackle decades of failed housing policy.

Shadow Housing Secretary John Healey said: “We’ve heard hand-wringing on housing from Theresa May before, but there’s nothing new here that will make a difference. After eight years of failure, it’s clear this Government has got no plan to fix the housing crisis. 

“Home ownership has fallen to a 30-year low, rough sleeping has more than doubled and the number of new homes built for social rent has fallen to the lowest level since records began.”

Wera Hobhouse, Liberal Democrat communities spokesperson, said: “If the Government are not willing to put up the public funds to solve the housing crisis and ensure the people get the home they need, then they need to look at where they are spending money elsewhere to fix the problem.

“Government incompetence and a refusal to enforce radical housing policies is putting this country on shaky foundations.”