Richmond Park was a byelection made in heaven for the Liberal Democrats. Their opponent – a prominent leave campaigner whose father had funded the anti-EU referendum party in the 1990s, and who upset many of those of a small “l” liberal disposition with the style and tone of his London mayoral campaign in the spring.

The constituency was a Lib Dem stronghold for over 40 years (until the vote collapsed, like almost everywhere else, in last year’s general election) where over 70% of voters had voted to remain in the EU, putting it in the top 10 pro-EU constituencies. Local Labour voters were long used to voting tactically for the local Liberal Democrat. All the party had to do was to turn this unusually propitious set of circumstances to its advantage.

But that does not mean that its victory can simply be dismissed as “a little local difficulty”. Not so. Because ever since Nick Clegg shook hands with David Cameron on the steps of 10 Downing St and formed the coalition, doing well in byelections – hitherto the Liberal Democrats’ forte – has been beyond them.

The last time the party was in this much electoral trouble was in the late 1980s following the Liberal-SDP merger

Even its success in retaining Eastleigh in 2013 masked a 14-point fall in the party’s vote, one of the biggest drops in support it had suffered in any post-second world war byelection. The party was saved from defeat by a Ukip surge at the expense of the Conservatives. But Richmond indicates that although the party is still languishing at just 8% in the national polls, it has at least put the searing experience of the coalition sufficiently behind it to restore its ability to make the best of a byelection.

Moreover, the Liberal Democrats’ success in Richmond is not an isolated one. It increased its share of the vote by 23 points in the Witney byelection in October. In local government byelections during the past three months, the party has on average enjoyed a 10-point increase in support, and has pulled off a number of seemingly remarkable victories.

Now the crucial question is whether the party can use the favourable publicity generated by its byelection victory in Richmond to begin to put itself back in the electoral frame more widely.

The last time the party was in anything like as much electoral trouble as the last few years was in the late 1980s following the acrimonious Liberal-SDP merger. And on that occasion it was a spectacular byelection victory, in Eastbourne in October 1990, that helped put the party back on the road to recovery.

The Liberal Democrats now need to use the publicity generated by Richmond to get voters to think afresh about the party once more. Any such a development would be unwelcome both to the Conservatives – who have the most seats that are potentially at risk from a strengthened Liberal Democrat challenge – and to Labour, who might fear that those of its supporters who are disillusioned with Jeremy Corbyn might begin to think they finally have somewhere else to go.

But if Thursday’s byelection could help open a new chapter in the story of British domestic politics, it is much less likely that the victory for an anti-leave candidate will have any immediate impact on the government’s pursuit of Brexit.

In arguing the case for holding a second referendum on Brexit, the Liberal Democrats are aiming at no more than a niche market. Polling from YouGov suggests that only around a half of those who voted to remain believe the government should hold a second referendum. However, thanks to the party’s long-standing pro-EU stance this is a niche that it is well-placed to win over.

However, it is not a big enough market to deflect a Conservative prime minister who knows that a majority of her voters backed leave, and only 26% of whom back a second referendum at the end of June.

Indeed, if the prime minister looks closely at the result, she will note that the 50% share won by the Liberal Democrats in Richmond is well below the 72% who voted to remain in June. Her job is to ensure that when the Brexit negotiations are over, most Conservative-inclined remain voters are sufficiently happy with the outcome that they will not be looking for a second referendum.

But that was already her task long before Zac Goldsmith opted to call what for him, at least, has proven be a fatally damaging byelection.