The Liberal Democrats gambled at the last general election that the popularity of their MPs would outweigh the general anger against the party. They were wrong, and lost most of their seats.

Now the tables have turned. In today’s by-election in Richmond Park & North Kingston, the Lib Dems are hoping that anger about Brexit can trump the charm of their opponent, Zac Goldsmith, the former Conservative.

The ballot is the first chance for voters in a pro-EU constituency to punish a prominent Brexit supporter. It has inspired an almost unprecedented mobilisation of Lib Dem campaigners, with about 200 volunteering in the constituency on Tuesday alone.

Activists say they have knocked on almost every door in the constituency four times, delivered more than 20 leaflets to some homes, and put up more than 600 placards in gardens. “I’ve never seen a positive feeling like this,” said Simon Drage, a party official.

In terms of placards, Sarah Olney, the Lib Dem candidate, would probably beat several chains of estate agents. Instead, activists on both sides place Mr Goldsmith, who won a 23,000 majority last year, as the marginal favourite.

The incumbent is standing as an independent after resigning from the Conservative party over its decision to back a third runway at Heathrow. But instead of campaigning vocally, Mr Goldsmith has refused media interviews.

“He has kept a low profile, which is odd,” said Christian Wolmar, the Labour candidate. “He is hoping that the memory of his name [will help him], that there won’t be a huge turnout . . . that it will pass off without much attention.”

Mr Goldsmith’s publicist said the by-election showed the MP had “kept his promise to his constituents” over Heathrow. But Mr Wolmar said: “The three main candidates agree on Heathrow. So what’s the point? The big unprompted issue on the doorstep is Brexit.”

If Mr Goldsmith does lose, it may reflect broader discontent with Prime Minister Theresa May’s government. “I think we need a better opposition,” said Jo Hawkins, a marketing consultant who previously supported Mr Goldsmith and is now planning to vote Lib Dem. “I was Remain, obviously. But I think we’re going with Brexit so we should just get on with it.”

Brexit “is part of it”, said one finance worker who has switched from supporting Mr Goldsmith to voting Lib Dem. “It’s more that I’m not happy with the Conservative government. I feel that this government is effectively unelected. I’d like a general election.”

Mr Goldsmith’s independent campaign has the advantage of not facing an official Tory candidate, after the party decided not to field one. But it cannot use Conservative party records of how residents have previously voted.

That means his supporters are “canvassing blind”, said one activist. They have also struggled to reach professionals who are out during the day and do not welcome callers on dark winter nights. “I’d campaign for Zac whatever party he was – I think he’s a brilliant local MP,” said Anne Speak.

When voters raised Brexit, she told them: “Zac had one vote just like I did, and that if you believe in democracy, then we have to respect the will of the people. He never campaigned in the borough [during the referendum].”

A Lib Dem victory “would show public opinion is fluid and unpredictable and that there are cross-currents”, said Nick Clegg, former leader. “It would increase that sense of brittleness and fragility about the Conservative government.” It might also lessen the chances of Mrs May calling a general election next year. An early election “would almost certainly return more Lib Dems at the expense of Conservatives and more Ukippers at the expense of Labour”, said Mr Clegg. “I just wonder if that’s the kind of parliament she wants.”

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