The Liberal Democrats have become the first of the big parties to launch their election manifesto, with a pitch to voters based on boosting the NHS and social care.

They also said that – unlike those of Labour and the Tories – their plans were fully costed.

Speaking at a glitzy launch event in north London, the party’s leader, Ed Davey, told voters that electing enough Lib Dem MPs would bring “a strong liberal voice pushing for these policies” and could make a notable difference even with an expected Labour majority.

The 116-page manifesto has been launched alongside a costings document, which pledges increased capital gains tax for very wealthy people, plus new levies on aviation, energy companies and banks.

Davey said this would pay for policies particularly focused on health and care, including guarantees about seeing GPs and dentists, free-to-access social care and more mental health support.

“We are putting forward a bold, ambitious and fully costed plan to tackle the healthcare crisis from top to bottom. This is a manifesto to save the NHS,” Davey told an audience of journalists and Lib Dem candidates and staffers.

As well as a series of green pledges, including an urgent programme of home insulation and retrofitting, and policies on the cost of living, such as a pledge on free school meals, the manifesto also takes in traditional Lib Dem areas such as political reform and Europe.

On the first, Davey said he hoped to “transform the nature of British politics itself”, both by introducing a proportional representation voting system, and by capping donations and thus “getting big money out of politics”.

On Brexit, while the Lib Dems’ primary pledge in the 2019 election was to annul the departure from the EU without a second referendum, the 2024 manifesto does not mention the issue until more than 100 pages in.

However, scattered through the manifesto are a series of EU-facing policies, including a pledge to expand freedom of movement for young people and returning to the Erasmus scheme for overseas study within the bloc.

Quizzed by reporters, Davey said that while rejoining the EU remained the party’s goal “in the long term”, this would only ever be done in stages, starting with moves to improve the existing trade deal with Europe – something the manifesto said would boost the economy.

“You can’t have a timeline – you’ve got to rebuild that relationship,” he said.

As the party released a document setting out its costings, it challenged the other main parties to do the same. They have been criticised for engaging in a “conspiracy of silence” over the scale of the economic challenge ahead.

The document says the Lib Dems could raise £26.9bn from measures including overhauling capital gains tax to raise £5.2bn for the NHS by 2028-29, as well as a windfall tax on fossil fuel companies and reversing tax breaks on bank profits.

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However, more than 25% of the total is made up of a planned £7.2bn to be saved by tackling tax avoidance and evasion, a financial source also cited by Labour and the Conservatives, but one experts have warned is difficult to harness.

The document also sets aside a planned average of £19.7bn a year in capital investment, which does not sit within the costings calculation, including £6.2bn for 150,000 new social homes a year, and £8.4bn for green investment.

The Lib Dems say they would also reform aviation taxes on international flights, raising a planned £3.6bn. They said families flying abroad one or twice a year would pay less, while those who travelled three times would pay about the same.

Those who took four or more flights abroad a year – less than 4% of the population, many of them on business flights – would pay more. The party hopes this could eventually encourage fewer flights.

Davey has already ruled out any increase in income tax, national insurance or VAT, but party sources insisted they were taking a “cautious” approach to their costings, which did not include the benefits of growth.