(Adds prices, analyst comments)

By Jamie McGeever, David Milliken and Patrick Graham

LONDON, June 27 (Reuters) - British 10-year government borrowing costs sank below 1 percent on Monday for the first time ever and sterling tumbled to a fresh 31-year low against the dollar as investors bet Britain's vote to leave the EU will trigger a Bank of England rate cut.

Billions of pounds were wiped off the value of British financial stocks, and analysts at several banks slashed their forecasts for the pound in the wake of Britain's vote on Thursday to leave the European Union.

Finance minister George Osborne said on Monday the economy would have to face up to "an adjustment" as it dealt with the fallout of 'Brexit'. Against a backdrop of sliding share prices and an uncertain economic outlook, investors sold sterling and sought the safety of government bonds.

"You'd have expected there to be some psychological barrier to gilts breaking through 1 percent, but not today," said Luke Hickmore, senior investment manager at Aberdeen Asset Management.

"Gilt yields just kept dropping. It's no wonder. There's no political leadership in the UK right when markets need the reassurance of direction," he said.

UK money and bond markets moved to price in lower interest rates, with swaps rates now almost fully implying a 0.25 percentage-point cut from the BoE by the end of the year.

The yield on 10-year UK government bonds tumbled to a new low of 0.934 percent, and two-year yields fell more than 10 basis points to a four-year low of 0.129 percent .

Sterling shed more than 3 percent against the dollar to a fresh 31-year low of $1.3221, and the euro rose more than 2 percent to 83.25 pence, its highest in more than two years.

The pound's fall on Friday was the largest in modern history, reaching more than 10 percent against the dollar at one stage, and was also the largest decline since at least the 1970s on a trade-weighted basis.

RBC Capital Markets now expect the BoE to cut rates by 25 basis points next month to 0.25 percent, and again in August down to 0.1 percent along with an additional 50 billion pounds of quantitative easing bond-buying stimulus. Several banks, including Goldman Sachs and Bank of America Merrill Lynch, cut their sterling forecasts too.

"With the Leave vote creating greater uncertainty over the outlook for the economy and BoE policies biased towards further easing/renewed QE, sterling is vulnerable to further near-term selling pressure," said Athanasios Vamvakidis, FX strategist at BAML.

"A push below $1.30 cannot be ruled out," he added.

Others, like Unicredit, reckon the pound will fall even further, perhaps as low as $1.20.

"The clear risk must be for further downside," said Neil Mellor, a currency strategist at Bank of New York Mellon in London.

"Uncertainty equals currency weakness, we know this, and there is no sense that this (sterling) is a value trade right now and that you have to get back in. It is too early for anyone to start calling a bottom."

Analysts at RBC Capital Markets pointed to the history of past sell-offs as pointing the way towards $1.20-1.25 for the pound by the end of the third quarter of this year.

So far, the fall against the euro and dollar of less than 10 percent is "very small" in the context of historical collapses, they said in a weekend note. "During eight independent price slumps over the last 40 years, sterling has on average fallen 18 percent," they said.

(Reporting by Jamie McGeever, David Milliken and Patrick Graham; Editing by Mark Trevelyan) ((jamie.mcgeever@thomsonreuters.com; +44 207 542 8510; Reuters Messaging: jamie.mcgeever.thomsonreuters.com@reuters.net))