Vince Cable has warned that Liberal Democrats are “being underestimated again” in terms of their potential to make gains in the European elections.

At a launch for the party’s election manifesto in Shoreditch, east London, its leader insisted they were “the biggest and best organised of the remain parties” in their preparations for the 23 May vote.

While climate change and cutting crime rates were high on the agenda, the event laid down the Lib Dems’ main aim to “stop Brexit” and hold a second referendum.

Earlier on Thursday Cable unveiled the slogan for the party’s campaign to remain in the EU – “Bollocks to Brexit” – a phrase so frank, he claimed, that a supporter had fainted upon hearing it.

In last week’s local elections the Lib Dems made big gains, leaving them in control of 18 councils and with 676 councillors.

Appearing on his 76th birthday, Cable, said: “I’m optimistic, buoyed up by last week. Everybody underestimated us, and I think they’re underestimating us again.”

He has confirmed that he plans to step aside after fighting the European election campaign in time for a new leader to be in place by the summer.

While he championed EU freedom of movement as “a precious thing”, the MP for Twickenham also said being a part of the union meant the country was better at tackling threats like data cooperation and protecting itself from being bullied by the US president, Donald Trump.

“We don’t deal with the Trump problem by grovelling and inviting him here for state business,” he added.

Also speaking at the launch, the former secretary of state for climate change and Lib Dem MP for Kingston and Surbiton Sir Ed Davey said: “Sometimes people say they don’t know what we stand for – I think they get the message now.”

Emphasising the importance of European arrest warrants, the EU’s law enforcement body Europol and other intelligence-sharing services in fighting “organised crime gangs, terrorists, murderers and rapists”, he said that “we also need to stop Brexit to stop the criminals.”

“The world’s most dangerous criminals want Brexit to go ahead,” he added. “The criminals know that the security deal that has not yet even been agreed is weak, pathetic and will make every British citizen less safe than now. Brexit is a thousand crimes or more waiting to happen.”

Investment in the NHS, building affordable homes to help young people on to the housing ladder and more funding for schools were also listed as key issues for the party.

Jo Swinson, Lib Dem MP for East Dunbartonshire, invoked the “tide of populism, with nationalism rolling in, Trump in the east and Putin in the west”.

She added: “Surely this is not the time to turn our backs on our closest allies, our closest neighbours who share our liberal values.”