By Patrick Graham

LONDON, June 7 (Reuters) - Sterling rose almost 1 percent against the euro and dollar on Tuesday after two polls gave a narrow lead to the "Remain" camp before Britain's June 23 referendum on membership in the European Union.

The pound had sunk to a three-week low in trade-weighted terms on Monday after two online surveys gave the "Leave" camp a 4 to 5 percent lead.

Support for remaining in the EU, however, had a one-point lead in both an online YouGov survey published for The Times newspaper on Tuesday and an ORB telephone poll for The Daily Telegraph of those who would definitely vote.

Dealers said a weaker tone to the dollar since poor U.S. jobs data on Friday helped the pound. So did better numbers on British retail sales and house prices, both published overnight.

"The Brexit storm probably isn't over yet for sterling," analysts from Belgium's Kredyt Bank said in a note to clients. "However, at least today, the news flow and the global context were constructive enough to trigger a rebound."

Sterling was last up 1.0 percent on the day at $1.4577 , up from $1.4352 on Monday and above long-term lows around $1.38 reached as the Brexit campaign got underway in February.

Still, the cost of protection against swings in the currency over the next month climbed to its highest since late 2008 on Monday, amid concern that support for Britain leaving the European Union is growing. It steadied around 22 percent on Tuesday.

Bookmakers have shortened their odds, with betting website Betfair putting the chances of a vote to leave at just over 30 percent, little changed from Monday. Odds at the end of last week had implied a 27 percent chance Britain would leave.

Credit Agricole strategist Jennifer Hau said those moves made betting on - or protecting oneself against - a Brexit through sterling options expensive.

"Our house view is for the UK to remain within the EU," she said. "However, should you wish to express the risk of a Brexit, we see better value in other currencies, such as euro pairs, given the potential spill-over impact into the euro."

The euro also fell around 1 percent to 77.84 pence .

"The debate is getting long, loud and messy," said Tobias Davis, head of corporate treasury sales at Western Union in London.

"A material breakout will be driven by any significant shifts in poll data one way or the other. Walking into the week of the 20th, there is still plenty room on the downside given February's $1.3833 low." (Editing by Larry King)

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