The Liberal Democrats have pledged to increase income tax by a penny for every earner to fund a £6bn-a-year cash injection for the NHS and social care.

In what was described as their flagship spending commitment of the general election campaign, the party’s leader, Tim Farron, said voters recognised the need to “chip in a little more” to address the “chronic underfunding” of healthcare.

Under the Lib Dem plan, 1p would be added to the basic, higher and additional rates of income tax and the rate of dividend tax from the next financial year, with the £6bn raised being ring-fenced for the NHS, social care and public health.

The proposal – which echoes the Lib Dems’ pledge from the 1990s to put a penny on income tax for education – will be seen as a clear attempt to capitalise on public concerns about the state of healthcare.

Theresa May has insisted the Conservatives have no plans for tax rises while appearing to back away from a previous pledge not to put up income tax or national insurance.

Farron said: “Theresa May doesn’t care about the NHS or social care. People are lying on trolleys in hospital corridors and she has done nothing. The Liberal Democrats will rescue the NHS and social care. We are prepared to be honest with people and say that we will all need to chip in a little more.”

The party’s health spokesman, Norman Lamb, said: “The NHS was once the envy of the world and this pledge is the first step in restoring it to where it should be. A penny on the pound to save the NHS is money well spent in our view.”

The Lib Dems pointed to an opinion poll finding from last year, which suggested 70% of voters would back a 1p rise in income tax if the money was guaranteed to go to the NHS.

According to figures released by the party, the rise would mean an increase of £33 a year – or less than £1 a week – for someone earning £15,000 a year, rising to £133 a year – or less than £3 a week – for someone earning £25,000.

At the top end, someone earning £150,000 would pay an extra £1,500 a year – or £29 a week – while someone on £250,000 would pay £2,500 a year, or £48 a week extra.

In the longer term, the Lib Dems said they would introduce a health and care tax to bring spending on both services together in a collective budget, and make clear on people’s payslips what was being spent on those services.

The party said it would seek to establish a cross-party health and care convention to review longer term sustainability of the health and care finances while setting up an office of health and care funding, similar to the Office for Budget Responsibility.