During the coalition years, Iain Duncan Smith came up with a plan: if unemployed people went on a demonstration, and the police stopped them for any reason, the officer should pass their names on to the Department for Work and Pensions, which could then freeze their benefits. After all, the minister’s reasoning went, if you had time to protest, you weren’t actively seeking work.

This was just one of the many David Cameron-era Tory proposals that the Liberal Democrats quashed before it ever saw the light of day. Every Lib Dem who worked in the coalition, whether as a minister or a special adviser, has a horror story about a policy they stopped or watered down – and usually the papers to prove it, too.

And so from time to time, Vince Cable’s team needs to respond to a news story by plundering their archives for anti-Tory material. A month or so ago, a former Lib Dem staffer got a phone call from the party’s press operation: could someone answer some questions about their time in government? To which the ex-staffer said: OK, but since you’re calling on a withheld number, you’ll need to get someone to vouch for you.

Perhaps, the former staffer suggested, Phil Reilly, the Lib Dems’ communications chief and a veteran of the party machine, was around? No, came the answer, he has moved on. What about Sam Barratt? Out at a meeting. Was Paul Haydon there? No. Haydon – who worked for the party’s last member of the European parliament, Catherine Bearder, before joining the press office – had moved on, too. After a while, this ex-staffer gave up and put the phone down.

The really troubling thing about this story is that I have heard it three times from three former Liberal Democrat aides. The names change, of course, but the point of the story – that the party machine has been stripped of much of its institutional memory – stays the same. The culprit, according to the staffers who have spoken to me, is Vince Cable. And the exodus is not just from the press office: the party’s chief executive, Tim Gordon, is among the heavyweights to have departed since the 2017 election.

Is this fair? Tim Farron, Cable’s predecessor as party leader, did not share Nick Clegg’s politics, but he recognised that he was inheriting a high-quality backroom team and strove to keep the main players in place. Reilly, who is now at the National Film and Television School, wrote not only Clegg’s concession speech at the general election in 2015, but Farron’s acceptance speech as leader a few months later.

The Liberal Democrats’ curse is that they have to fight for every minute of press and television coverage, so the depletion of their experienced media team is particularly challenging. But their problems go beyond the question of who works at the George Street headquarters in London. As party veterans note, Cable leads a parliamentary group whose continued existence is as uncertain as it was when Paddy Ashdown first became its leader in 1988. The difference is that Ashdown had a gift for identifying issues that the main political parties had neglected. That gave him a greater media profile than his party’s standing warranted.

There is no shortage of liberal and green issues on which Cable could be more vocal: the right to die, for instance, or the legalisation of cannabis. He could even take a leaf from Ashdown’s playbook and set out a bolder approach on income tax than either Theresa May or Jeremy Corbyn. While none of these issues command anything resembling majority support, they are distinctly more popular than the Liberal Democrats. They would also get the party talked about more often. At present, it is being ignored.

These complaints will receive a greater airing if the Lib Dems have a disappointing night at the local elections on 3 May. The party hopes to gain ground in Manchester and retain the Watford mayoralty, but fears it will lose control of the council in Sutton, south-west London. It expects to make little headway overall.

So what else could be done? If you gather three Liberal Democrats in a room, you will hear at least five opinions about what Cable is getting wrong. But the party’s problems neither start nor end with its leader. Cable inherits two difficult legacies: first, thanks to Farron, his party is committed to an all-out war against Brexit. In 2016, that policy successfully gave a shattered party a reason to exist, and some hoped that the Lib Dems could recover ground by wooing disgruntled Remainers. Last year’s general election changed the game, however. The two big parties took their highest share of the vote since 1970, squeezing the Lib Dems to a dozen MPs. That simply doesn’t give the party the numbers to “stop Brexit” – therefore, they feel to many like a wasted vote.

Why not drop the commitment to a second in/out EU referendum? Because one of Farron’s successes was attracting pro-European new members – and thanks to the party’s ultra-democratic constitution, these hardcore Remainers can keep that commitment in place for as long as they wish.

The legacy of coalition is even more difficult to address. In policy terms, the Lib Dems can point to great achievements in government: across every department, there are examples of Duncan Smith-style cruelties that the party prevented.

Yet there is no electoral coalition to be won from voters who are pleased and grateful that hypothetical horrors didn’t come to pass. More than half of voters still regard the Lib Dems’ participation in coalition as a reason not to back the party. That might change as the memories fade, but for now the party’s last spell in government is a significant barrier to gaining the chance to have another one. Even a fresh, young and charismatic leader – with a superb, experienced team – would struggle with such a poisoned inheritance.