Liberal Democrat leader Sir Ed Davey has challenged his party to “tear down” the Conservatives’ “blue wall” in order to help oust Boris Johnson from Downing Street.

In his keynote address at the Liberal Democrat conference on Sunday, Sir Ed said the Tories would only lose power at the next election if his party took seats off them.

“Make no mistake: the electoral arithmetic is clear,” he said. “These Conservatives can’t be defeated next time unless we Liberal Democrats win Tory seats.”

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Sir Ed pointed to his party’s recent victory at June’s by-election in Chesham and Amersham – when they took the constituency from the Conservatives – as showing how “even in deepest, bluest Buckinghamshire the Tories can be beaten”.

“In Chesham and Amersham, we knocked out one blue brick; now it’s up to us to tear it down,” he added.

In a series of attacks on Mr Johnson and his government, Sir Ed claimed that many in traditionally Conservative-supporting areas “just don’t feel that Boris Johnson represents them, or shares their values”.

“They’re not convinced the prime minister is competent – or worse still, decent,” he added.

And he said people who had voted Tory all their lives “now feel completely let down” and “betrayed”.

Sir Ed said part of the reason for Lib Dem success in Chesham and Amersham was a “groundswell of frustration and discontent from people who feel ignored and taken for granted by this Conservative government”.

He appeared in front of around 150 people in London’s Canary Wharf in his first leader’s speech in front of a live audience, although most of the Lib Dem conference has been held online.

Sir Ed attacked the Tories’ cuts to Universal Credit, the reduction in the UK’s foreign aid budget, Conservative immigration policies and the government’s handling of the Afghanistan crisis.

And he also took aim at new Justice Secretary Dominic Raab, whose Esher and Walton constituency is one of the Lib Dems’ key targets ahead of the next election.

Sir Ed joked that the former foreign secretary – who was widely criticised for being in Greece as Afghanistan fell to the Taliban – only accepted his three new jobs at last week’s cabinet reshuffle “on the basis that three jobs would come with three times the holiday entitlement”.

The Lib Dem leader accused Mr Johnson of “steering us all into another terrible crisis” – after Brexit and COVID-19 – as UK businesses suffer supply issues and labour shortages.

He claimed ministers had “ignored all the warnings” about the government’s Brexit deal and new immigration rules.

And Sir Ed quipped: “To be fair, this is one time Boris Johnson has actually delivered; he said he wanted to ‘f*** business’, and he has well and truly f***** them.”

He called on his party to think back to 1992, when the Tories last won a fourth term in office, to remember how then Lib Dem leader, the late Paddy Ashdown, called for the party to “be the catalyst, the gathering point for a broader movement dedicated to winning the battle of ideas which will give Britain an electable alternative to Conservative government”.

“That was the role of the Liberal Democrats then and it is the role of the Liberal Democrats today,” Sir Ed said.

“Boris Johnson is not a prime Minister worthy of our great United Kingdom. His Conservatives are not a government worthy of the British people.

“This prime minister and these Conservatives have got to go.”

Although the Lib Dems and Labour discussed a coalition of their parties prior to the 1997 general election, Sir Ed has recently said he is “very sceptical” of a possible deal between current opposition parties.

Outlining his “fair deal” offer to British voters ahead of the next election in his speech, Sir Ed outlined commitments on climate change – such as banning new oil, gas and coal companies from the London Stock Exchange – as well as plans to replace business rates with a land tax and a proposal to allow unpaid carers and those they care for to have their own care budget.

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In the major policy announcement of his speech, Sir Ed called for the government to match what their own education adviser, Sir Kevan Collins, urged ministers to do and put at least £15bn into a post-pandemic catch-up fund for pupils.

He said schools should be able to spend the cash “as they see best”, while the Lib Dems have proposed that £5bn of the money over a three-year programme should be handed to parents in the form of catch-up vouchers.

“Parents could choose to spend it with their child’s own school – on an after-school homework club, on one-to-one tuition, on special extra-curricular activities from sports to music lessons, provided for that child by their school,” he said.

“Or parents could choose to spend it on tuition they organise. Or with a music teacher they find. Or on therapy and counselling.

“As long as it was supporting the education and well-being of their child, it would be the parents’ choice.”