Jo Swinson arrives at probably the best time to be a Liberal Democrat for a decade. In May the party posted a record European election result, attracting both Labour and Conservative voters disaffected by their own parties’ divisions over Brexit. A few weeks earlier local elections saw the party gain hundreds of seats and control of a series of councils in England. The party hovers near the top of the polls. Ms Swinson’s job will be to keep it there.

This has been a remarkable turnaround. In 2015, as the Oxford academic Tudor Jones notes in his forthcoming book The Uneven Path of British Liberalism, the Lib Dems suffered an electoral collapse as great as the two great vanishings that the Liberal party managed in the 20th century. What almost finished the Lib Dems off was not just their hand in austerity, but the party’s perceived political irrelevance in the minds of a majority of British voters. If history was any guide, the road back to significance would have been a long one.

Yet the first female leader of the Lib Dems will have the wind in her sails – thanks in large part to the party’s implacable opposition to Brexit. One poll suggests the party will capture Brecon and Radnorshire in a byelection, helped by other remain parties standing down. If the alliance was replicated across the country, experts suggest, possibly 150 seats could be won. That of course depends on how Labour calibrates its response to Brexit. The Lib Dems’ strength is that they chose early on to oppose it in stark terms. Not only did this put the party back on the map, it also reminded the public about its traditions; the Liberal party was the first political party to declare public support for British membership of what was then the European Economic Community.

Whatever the pretensions to be the next prime minister, the new Lib Dem leader will lead just 11 MPs in parliament – making it the fourth force in Westminster party politics. While they lack the parliamentary machinery of the big two parties, the Lib Dems must strive to play a part in moulding the future. This will mean they will have to work out how to be more than just a protest vote against Labour and the Conservatives, at a time when populism is in the ascendancy. Ms Swinson could do worse than follow in the social liberal tradition of Beveridge and Keynes. There is room in UK politics for a party that combines social democratic economics and an uncompromising anti-Brexit message with a strong commitment to constitutional reform, environmentalism and civil liberties.

It is true that liberal ideas across Europe are being tested by the politics of fear. But the Lib Dems must find convincing answers to the questions about how societies can manage inequality, champion immigration and defuse nationalism’s incipient threat. So far, apart from the party’s Brexit message, the Lib Dems have largely offered an unadventurous and conservative response to the gravity of the problems afflicting the nation. While the policy message will need to be honed, Ms Swinson will also have to prove that she can be an effective communicator of the Lib Dems’ appeal as a positive choice in British politics.

The sterility of our current politics may not last, though it is hard to see how it might end any time soon. What is up for grabs in politics is which party will be at the centre of progressive change in Britain. In terms of its parliamentary weight and policies, Labour has been the most effective vehicle for the fair and just transformation of Britain. For Ms Swinson to change that will require a stable base of voters and an attractive bedrock of principles.