Ed Davey has unveiled a plan for a £17bn income tax cut in a speech aimed at shoring up the party's support among former Conservative voters, but which risked disappointing some Liberal Democrat MPs who want a bolder vision for the party.

Addressing the party's annual conference in Brighton, the Lib Dem leader said the proposal, which would eventually increase the threshold for paying income tax to £15,000 and raise the level at which people pay the 40p higher rate by about £6,000, would be paid for entirely by increased growth.

This growth, the Lib Dems argue, would be created through rejoining the EU's single market and customs union.

As making a deal with the EU would take time, the actual tax cuts would only happen in the final year of a parliament, potentially as late as 2034, costing £17bn. In the interim years, thresholds would be raised by inflation, thus keeping levels effectively stable.

There would also be a smaller increase to the 45p additional rate of tax, currently payable above £125,000.

Setting out what he described as "trusting people to spend their own money, not telling them the state knows best", Davey took aim at what he called "the post-Brexit stealth taxes" of frozen thresholds, notably on the higher 40p rate.

"Thirty years ago, just 2 million people paid it. Now it's 9 million," he said. "A tax band designed for stockbrokers is now holding back teachers and nurses. That's not fair. It's not right."

The plans mark a distinct shift in the party's fiscal approach. While it is eyecatching and could appeal to the many former Conservative voters who backed the Lib Dems in 2024, helping them take 60-plus Tory seats, it is likely to cause unease among some of the party's MPs.

A number of them have called privately for a more ambitious and comprehensive vision of what the party stands for, amid polling that shows most voters do not have much of a sense of this.

Davey's advisers, however, argue that the cost of living is the subject that most affects many voters, and that tax cuts – even up to eight years in the future – directly address this.

Other elements of the speech included previously-trailed new policies, including a proposal for a global nuclear-style non-proliferation treaty to halt the development of super-intelligent AI.

The tax-cutting plan is predicated entirely on the EU allowing a swift deal on single market access, which could become even more difficult if rightwing populists take power in more EU states, and on this then increasing growth.

The Lib Dems insist the numbers stand up, saying they are based on a report from an independent economics consultancy, which calculated that a deal with the EU could generate 0.5% growth in the first fiscal year alone.

Reform UK has already pledged to increase the personal tax allowance to £15,000, paid for in part by significant cuts to social security.

Davey noted this in the speech, saying: "Think about that. Reform say you can have a tax cut, but only if they get to punish disabled people at the same time. We say no. We can cut taxes and support the most vulnerable people in our country."

Opening his speech with a warning that black-shirted, and balaclava-wearing far-right protesters who gathered in Dover and Portsmouth "would tear our country apart", Davey compared groups such as Patriot Platform to Oswald Mosley's fascists in the 1930s, the National Front in the 70s and to Nick Griffin and the BNP.

"Each time, they tried to turn neighbour against neighbour, tried to pit community against community, tried to turn our streets into battlegrounds," he said. "But we didn't let them. The British people said no."

He said this time, far-right vigilantes were not acting in isolation, but were the most visible part of a far-right threat that was "extremely well funded" and promoted by figures such as Elon Musk and given credibility by "cynical politicians like Nigel Farage".

Davey slammed Farage as a cynical politician who was "not just willing, but eager to fan the flames of hatred and intolerance to make himself richer".

He said: "It is the worst of Trump's America. We must not let it become Farage's Britain." Pointing to the £72m donations Reform had received from two crypto billionaires, Davey added: "If there was any doubt before, there can't be now. We are in the fight of our lives. And it is a fight we must win."