Many of the Liberal Democrat campaigners who scored stunning results for us last week are now running local government around the country. Our 100,000 membership is strongly committed to carrying that success through into the European elections in a little under three weeks’ time. We have a clear mission to stop Brexit.

All eyes are at the moment on Nigel Farage’s Brexit party, which will undoubtedly do well if it becomes the main political vehicle for strongly committed Brexit supporters. But on the other side of the argument, there is a strong vehicle for committed remain voters. I hope and expect that they will turn out in force, welcoming a clear, honest message from the Liberal Democrats.

Even now, though, people inside and outside the Lib Dems are asking me if there is anything that can be done to stop the remain vote fragmenting. I had hoped that those of us firmly backing a people’s vote could run jointly, but a cocktail of naivety, hurry and inflexible electoral rules contrived to stop it happening.

This will likely be remembered as a missed opportunity, and it represents a risk to the remain cause. Although European elections operate on a form of proportional representation, the system is still very unforgiving to vote-splitting. The difference between one party winning 20% and two parties winning 10% each can be stark. While 20% probably wins a seat or even two, 10% invariably wins nothing at all, even in the larger regions where more seats are up for grabs.

The more competitors on the same territory the greater the risk that, by failing to hang together, we hang separately

The parties having failed to get together, the only hope left is that voters will make a hard-headed assessment about who can make an impact. Having won clear victories around the country and almost 20% of the vote nationally, we go into the European elections as the clear gathering point for remainers. And Lib Dem MEPs have a strong record of campaigning on the environment, consumer protection and animal welfare.

Labour, by contrast, are still working out what to write in their election leaflets, carefully reviewing, revising, and caveating pro- and anti-Brexit versions. With Jeremy Corbyn having so badly let down millions of Labour supporters, and Conservative voters aghast at the track the country is on, there is much to play for so long as remain votes are not wasted.

Lib Dems have for decades been on the wrong end of the “wasted vote” argument in which people say they would support us but for their belief that too few other people are doing so. It is uncomfortable to proffer the same vicious circle in our own defence, but it is crucial. In the light of last week’s results, Liberal Democrats clearly can win, and we need everyone who wants to stop Brexit behind us.

Once the immediate bunfight for votes is over, liberals and social democrats in all the parties need to look afresh at how we make an impact when a general election finally comes. Millions of voters are politically homeless and looking for a voice.

Yet seizing the opportunity will be about more than brands and rhetoric. It takes infrastructure, volunteers and sheer hard work. The first-past-the-post system makes a general election an existential threat to any force which doesn’t have a serious ground campaign. Meanwhile, the more competitors there are on the same territory the greater the risk that, by failing to hang together, we all hang separately.

But there is hope: last week’s results signal the return of Lib Dem MPs in parliamentary constituencies as diverse as North Devon, Winchester, Chelmsford, Harborough, Penistone and Stocksbridge, Southport and Leeds North West (to name just a few). In the task of rebuilding the liberal centre ground of British politics, the Liberal Democrats are once again indisputably the foundation stone.

Vince Cable is leader of the Liberal Democrat party