By Andrew Osborn

LONDON (Reuters) - Fewer than 100,000 residents of an English town that hardly anyone outside Britain has heard of will vote on Thursday in an election that could help determine the political fate of the country's deputy prime minister and, ultimately, its government.

The poll to choose a member of parliament for Eastleigh may prove make-or-break for Nick Clegg's leadership of the Liberal Democrats, the junior member of Britain's two-party coalition.

"Most by-elections are events of only fleeting interest. Some are sufficiently dramatic to linger a while in the memory. Only a few truly matter. Eastleigh could be one of these," Peter Kellner, the president of YouGov, the pollster, said.

On Wednesday, during last-minute campaigning in Eastleigh, Clegg predicted his party was "on the cusp of a great victory".

If he is right, the pressure he is facing, from the media and from within his own party, may ease. But if his Conservative coalition partners pip the Liberal Democrats, or the UK Independence Party pulls off a surprise victory, his leadership may be challenged ahead of a party conference next week.

Many Liberal Democrat supporters have become disenchanted with their party's alliance with the Conservatives, arguing it has betrayed core values on the altar of political expediency. Much of that criticism has been directed at Clegg.

"If the Tories do win, then we may well look back in years to come as the contest that marked the beginning of the end of the current coalition," said YouGov's Kellner.

NOT REFLECTIVE OF NATIONAL TREND

The Eastleigh vote does not reflect national sentiment - the opposition Labour party leads in the polls nationally with the Liberal Democrats trailing in third or fourth place.

Most opinion polls show Clegg's party the narrow favorite to win, with the Conservatives running a close second and UKIP third. But its lead in the polls - 5 percent - is within the margin of error and a last-minute swing in favor of the Conservatives could rob it of victory.

The election comes at a time when Clegg's leadership of his leftist party, without whom the rightist Conservatives cannot govern or pass legislation, also faces specific pressures.

A sex scandal that has ensnared Chris Rennard, his party's former chief executive, has raised difficult questions for Clegg about what he knew about the imbroglio and when and how he dealt with it, amid accusations of a cover-up.

Rennard strongly denies the accusations, which center on allegations of sexual misconduct towards female party workers, while Clegg says he was only previously aware of "non-specific" and "anonymous" allegations which could not be acted upon.

The circumstances surrounding the Eastleigh vote, which comes almost two and a half years before a general election, are embarrassing for Clegg's party.

The seat, one of 650 in Britain's lower house of parliament, was won by the Liberal Democrats in 2010. But the victor, Chris Huhne, who went on to become energy minister, had to resign on February 4 after a lawsuit over a speeding offence.

Huhne pleaded guilty to perverting the course of justice and now faces jail.

(Editing by Louise Ireland)