The survey, published on Monday, found that 17 percent of those with more than £250,000 ($391,025) in savings and investments wanted to move abroad in the next two years, up from 14 percent six months earlier.
The most popular destination for the rich exiles was France (21 percent), followed by Spain (15 percent) and the US (11 percent).
Three-quarters of those questioned (73 percent) thought that crime was a bigger problem in Britain than other developed countries.
"Sadly, it seems August's riots, tax increases and a rising cost of living have cast a pall over life in the UK for some wealthy people," said Nicholas Boys-Smith, managing director of Lloyds TSB International Wealth in a statement.
"It may reignite fears of a 'wealth drain' from our economy as rich people seek pastures new," he said.
42 percent of those questioned named tax as a reason for leaving, up from 35 percent six months ago. Cost of living was a factor for 52 percent, up from 31 percent.
Research in January 2011 suggested that 4.6 percent of the UK population have over £250,000 in savings and investments, which equals around 2.8 million people.