Complacency is threat to Britain's stay-in-EU campaign - strategist

* Crosby says EU referendum hangs in balance

* Opinion poll shows 'Out' has 2 pct point lead

* Crosby says risk for 'In' is complacency

* Undecideds worried about immigration

* Sterling falls a percent on Brexit worry (Adds bookmaker's odds)

By Guy Faulconbridge

LONDON, March 15 (Reuters) - The biggest risk for the campaign to keep Britain in the European Union is that people who wish to stay in the bloc may not show up to vote on the day of referendum in June, Prime Minister David Cameron's election strategist says.

The result was still in the balance, Lynton Crosby said, commenting on an opinion poll on Tuesday that gave the "Out" campaign a 2 percentage point lead.

Sterling shed 1 percent after the ORB poll for The Daily Telegraph showed 49 percent of respondents would vote to leave the EU while 47 percent wanted to stay in the 28-country bloc.

Crosby, who helped Cameron unexpectedly win outright victory in a national election last May, said engagement would be the key question of the June 23 referendum.

"The real risk for the Remain campaign is complacency," Crosby, an Australian political strategist who uses extensive polling to target voters in election campaigns, said in an article in the newspaper.

"What is clear is that this campaign has a long way to run, and despite what voters currently believe, the outcome really is in the balance," Crosby added.

Among those who definitely plan to vote, support for leaving rose to 52 percent against 45 percent to stay, the ORB poll showed.

William Hill (Other OTC: WIMHF - news) 's betting odds indicate a 75 percent chance of Britain remaining in the bloc it joined in 1973 with a 31 percent chance of an exit. William Hill said 51.7 percent of the money staked was for Britain to remain in the EU.

"IN THE BALANCE"

Crosby, who also ran Boris Johnson's successful mayoral election campaigns in 2008 and 2012, said the biggest problem for "In" was that many pro-membership voters would not turn up to vote.

He said the ORB the poll showed 76 percent of "In" voters expected Britain to stay in the bloc but that a quarter of them were unlikely to vote.

"It (Other OTC: ITGL - news) is obvious they have a preference for the UK to remain in the EU, but the outcome of the referendum is not currently important enough to them to motivate them to show up," Crosby said.

"This demonstrates the consequence of the outcome lacking personal relevance to them."

Crosby said the poll showed a third of voters who were undecided or likely to change their mind said that immigration was the issue preventing them from voting to stay in.

Crosby said the "Out" campaign had a different challenge - half of such voters think Britain will remain inside the EU so they are sceptical their vote can influence the outcome.

"Leave voters still do not believe their vote can affect the outcome, their engagement and motivation may tail off," Crosby said.

The poll of 823 people, interviewed by telephone between March 11 and March 14, found that 4 percent of respondents overall, and 3 percent of those definitely planning to vote, were undecided.

"One of the keys to winning a campaign is focusing on the strengths rather than the weaknesses that voters perceive," Crosby said.

"For the Remain campaign this means demonstrating the importance of the economy, while for the Leave campaign, this means demonstrating the impact of immigration. This is largely what we have seen so far." (Editing by Catherine Evans and Angus MacSwan)