LONDON — Scotland’s nationalists wasted no time: Just minutes after the country’s leader, Nicola Sturgeon, called on Monday for a new independence referendum, a website went live asking people to show their support on Twitter and donate to the campaign.

By Tuesday morning, 204,345 pounds, or about $249,000 — more than a fifth of the £1 million target — had been raised; pro-independence banners in Scotland’s blue-and-white colors had gone up across the country; and celebrities were offering support, including the actor Alan Cumming, who shared a Twitter post by Ms. Sturgeon, with the comment “It’s showtime!”

It was an early glimpse of the Scottish nationalists’ formidable campaign machine, evidently little diminished since the last referendum, in 2014. Support for independence rose from about 27 percent at the start of that campaign to 45 percent at the final count.

Since then, opinion polls suggest, support for independence has edged up again, leaving Scots split almost evenly. Nationalists seem convinced that they can win this time, thanks to Britain’s vote to leave the European Union, known as Brexit. And unlike Prime Minister Theresa May’s government in London, which is already stretched by the monumental task of negotiating a divorce settlement with 27 other European governments, Ms. Sturgeon’s troops are ready: Party membership quadrupled after the last referendum and increased further after the decision to quit the European Union.