LONDON (Reuters) - Voters' ideas of the impact of the European Union on life in Britain are mistaken in many areas, from the level of immigration to non-existent rules over barmaids' cleavages, according to a survey published on Thursday.

With just two weeks to go until they vote in a June 23 referendum on whether to stay in the EU, Britons are still evenly divided on how to vote, polls show. Immigration and the economy have become key battlegrounds for the "In" and "Out" campaigns.

But Thursday's survey by Ipsos MORI and the "UK in a Changing Europe" initiative found many voters' ideas are inaccurate.

For example, on average Britons think EU citizens make up 15 percent of the total UK population, three times the real level of about 5 percent.

Asked about EU regulations, which Out campaigners have described as excessive and interfering, 15 percent believed at least one mythical EU rule put to them such as that the EU had banned barmaids from showing too much cleavage.

"There are obviously still high levels of ignorance about the EU, which is troubling so close to the referendum," said Anand Menon, Director of UK in a Changing Europe, an initiative promoting independent research on UK-EU relations.

"It's now more imperative than ever that the public can be provided with as much factual information about the EU as possible before they cast their vote." berxit

The level of welfare payments to children living elsewhere in the EU, one of the central planks in Prime Minister David Cameron's renegotiation of Britain's EU relationship earlier this year, was also hugely overestimated by many people.

The survey found 14 percent of Britons believed 30 percent of all UK child benefit payments went to children abroad, 100 times the actual level of 0.3 percent. Nearly a quarter of people thought the level was 13 percent.

Voters also overestimate how much Britain pays in to the EU budget compared to other members and underestimate how much investment into Britain comes from EU countries, Ipsos MORI said.

The survey also found that one of the In campaign's key messages, that Britons will be worse off post-Brexit, was not persuading everyone. Only a quarter of voters believed their own living standards would be reduced by leaving the bloc.

Ipsos MORI conducted 1,000 interviews online April 29 to May 5 and a further 1,083 between May 27 and 30.

(Reporting by Kylie MacLellan; editing by Stephen Addison)