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This combination picture shows (L-R) Deputy Prime Minister and Leader of the Liberal Democrats Nick Clegg, opposition Labour Party leader Ed Miliband and British Prime Minister and Leader of the Conservatives David Cameron on the campaign trail on May 6, 2015.-/AFP / Getty Images

Amy Herbert has never met Robert Knight, but on Thursday she will go to a polling station in southwest England and – acting against her own political beliefs – cast a ballot for Mr. Knight's preferred party, the Liberal Democrats. She'll do so trusting that Mr. Knight, an ordinary voter like her, will reciprocate by marking his own ballot for the party she really supports, the Labour Party, in his own constituency.

Thursday's election in the United Kingdom is unlike any of those held before it. Every polling firm says the result is too close to call, and a hung Parliament is considered all but a certainty. At the end of an almost six-week campaign, few were daring Wednesday to predict what the country's next government will look like.

With the race so tight, voters are being pressured to vote tactically – that is, to cast their ballots with one eye on the candidates in their local constituencies, and the other on the big picture of how the each race could affect who becomes prime minister.

Many Britons, like Ms. Herbert and Mr. Knight, are taking the idea a step further and sending their votes to wherever they think it will have the greatest impact. Tens of thousands have entered into informal pacts – brokered by vote-swapping websites that have sprung up for the election – where each person promises to vote for the other's party of choice.

The voting on Thursday is expected to be followed by days or weeks of political uncertainty, with Conservative Leader David Cameron and Labour Leader Ed Miliband mounting rival efforts to build enough support in Parliament to claim the prime minister's job.

A final "poll of polls" published by the website – taking into account the work of nine different polling companies – gave the Conservatives the slimmest of leads with 33.9 per cent of the popular vote, to 33.4 per cent for Labour. The rest of the vote looks set to be scattered across an unprecedentedly wide landscape of challengers.

The same website forecasts the Conservatives will win 275 seats to 266 for Labour, leaving both well short of a majority in the 650-seat House of Commons. The separatist Scottish National Party (SNP) is expected to win the third-largest number of seats, followed by the centrist Liberal Democrats.

The rise of vote swapping is just the latest indent the Internet and social media have made on election campaigns. The idea's popularity in the U.K. also highlights flaws in the winner-take-all constituency system (known as first past the post), which can leave voters living in so-called safe seats, ones that rarely change hands between parties and make constituents feel as if their opinions don't matter. The first-past-the-post system is also used in Canadian elections.

Ms. Herbert's own constituency of Chippenham is considered a two-way race between the Conservatives and the Liberal Democrats, with the Labour candidate expected to finish a distant third. Ms. Herbert, a 24-year-old teacher angered by cuts to the education system carried out by the incumbent Conservative-Liberal Democrat coalition government, said she didn't want to vote for either party, but worried a vote for Labour would be "massively wasted" in Chippenham.

Mr. Knight felt the same way about his plan to vote for the Liberal Democrats in nearby Southampton Test, where only the Conservative candidate is seen as having a chance of unseating the Labour incumbent. Both found themselves on the newly launched website, which connected them and led to the agreement that will see Ms. Herbert hold her nose to vote Liberal Democrat in Chippenham while Mr. Knight marks his ballot for Labour in Southampton Test.

Ms. Hebert admitted she felt some nervousness about the arrangement since she doesn't know anything about Mr. Knight besides his name. "I hope he's using the system for the same reason I am – trying to keep the Conservatives out of government – but since my vote would have been wasted anyway, there's actually not a lot to lose," she said.

Tom de Grunwald, a television producer who co-founded, said the website has connected "thousands" of voters unimpressed by the choices in their local constituencies. "It's an enormously febrile electoral landscape and … people are very interested in making their vote count in this election," said Mr. de Grunwald. He said the idea for the website was born out of his own frustration with the voting options in his constituency during Britain's last election in 2010.

Mr. de Grunwald's website is politically neutral, asking users which party they most want to vote for – and which second party they would be willing to vote for in a trade – then attempting to match them with someone willing to make that precise swap.

Other efforts are openly partisan. One popular site, – which connects Green Party supporters willing to vote Labour in tight races with Labour supporters willing to vote Green in constituencies where the result isn't in question – claimed to have arranged almost 20,000 vote swaps as of late Wednesday.

Another website briefly attempted to "unite the right" by co-ordinating vote swaps between backers of the Conservatives and the more radical U.K. Independence Party (UKIP). But supporters of the two parties proved hostile to the idea and the website didn't appear to be functioning on Wednesday.

Mr. de Grunwald said he hopes the rise of vote swapping – which he compared to the Airbnb website that connects travellers with available rooms in their destination city – will generate discussion about the first-past-the-post electoral system both in Britain and Canada. He said he's already in discussion with Canadian activists about setting up a vote-swapping website ahead of the Oct. 19 federal election.

John Curtice, professor of politics at Strathclyde University in Glasgow, said the rise in strategic voting – and rise of parties such as UKIP, the Greens, and the SNP – illustrated how the rules of British politics were shifting under the clumsy feet of the Conservatives and Labour.

"Voters have simply refused to accept that the election is a choice between only two parties," he said. He said the election was an "unpopularity contest" between Mr. Cameron and Mr. Miliband, with neither leader managing to convince the electorate of their vision to lead the country.