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UPDATE 4-Polls on eve of UK election suggest PM May will boost majority

* Britain holds national election on Thursday

* Flurry of last-minute polls give relief to May

* Conservatives likely to increase majority - polls

* May called election to strengthen hand in Brexit talks (Adds Survation poll)

LONDON, June 7 (Reuters) - Prime Minister Theresa May is on course to increase her majority in parliament in Britain's election on Thursday, opinion polls showed on Wednesday, suggesting her gamble to call the vote to bolster her position in Brexit negotiations will pay off.

May has seen her once-commanding lead over the Labour Party and its veteran hard-left leader Jeremy Corbyn narrow sharply since she surprised almost everyone by calling a snap election in April.

Of six polls published on Wednesday, two showed the Conservatives widening their lead over Labour, two showed a narrowing and two were unchanged.

But they mostly suggested she would increase the small majority she inherited from David Cameron last year, shortly after the surprise referendum decision to take Britain out of the European Union.

Polling firm ICM said Conservatives' wide lead of 46 percent to 34 percent for Labour would give May a majority of 96 seats, up sharply from the working majority of 17 she has had until now and bigger than any Conservative majority since the days when Margaret Thatcher was prime minister.

The Independent newspaper said the 44-34 lead for the Conservatives in a poll it commissioned from ComRes would give May a majority of 74.

YouGov, which found the Conservatives' lead had increased to seven percentage points from four during the weekend, also said May would bolster her power in parliament.

"The seven-point Conservative lead is the same as at the previous election, but we think it is likely they will nevertheless be returned with an increased majority," YouGov Director Anthony Wells said.

The polls were conducted after a deadly attack by Islamist militants in London on Saturday.

ICM and ComRes have tended to give the Conservatives bigger leads than other polling firms.

At the other end of spectrum, Survation said the Conservatives' lead stood at just one percentage point, echoing two polls it published in recent days which called into question whether May would get a majority at all.

Polling experts have said the main difference between the polls which give the Conservatives a big lead and ones such as Survation which suggest a tighter race is largely down to varying estimates of how many young voters, who typically support Labour, are likely to actually vote on Thursday.

Investors took the latest findings as a sign May was likely to emerge victorious, giving her a boost before the start of Brexit talks this month. Sterling rose by nearly half a cent against the U.S. dollar after the ICM poll was published.

GAMBLE

ComRes Chairman Andrew Hawkins said May was in the clear after securing the support of around 2 million voters - worth about six percentage points in the polls - who backed the anti-EU UK Independence Party in Britain's last election in 2015, and who have warmed to her tough stance on negotiating Brexit.

"Despite Mrs Mays ratings taking a hit during the campaign, older voters in particular have stuck with her party and it appears that the electoral gamble is about to pay off," he said in a blog.

The big differences in the poll findings in the run-up to Thursday's vote have added to skepticism among critics of polling who point to how the industry largely failed to accurately predict the outcome of the 2015 election and last year's referendum vote to exit the EU. (Reporting by William Schomberg and Georgina Prodhan; Editing by Andrew Roche and Jonathan Oatis)