* UK CPI falls to 2% in May from April's 2.3%
* Services inflation drops less than expected to 5.7%
* Economists do not expect BoE to cut rates until August
* UK inflation peaked at 11.1% in October 2022
(Adds new market reaction, quotes and factors behind inflation fall in paragraphs 4-5, 17-18 and 21-22)
LONDON, June 19 (Reuters) - British inflation returned to its 2% target for the first time in nearly three years in May, but strong underlying price pressures all but rule out a pre-election interest rate cut.
While Prime Minister Rishi Sunak welcomed the fall in headline inflation in May, it has likely come too late to turn around his fortunes in British elections on July 4 or to prompt a Bank of England rate cut on Thursday.
Office for National Statistics data showed services price inflation, which the BoE thinks gives a better picture of medium-term inflation risks, was 5.7%. That was down from 5.9% in April, but higher than the 5.5% economists had forecast in a Reuters poll or the 5.3% predicted by the BoE last month.
Sterling rose modestly against the dollar and the euro after the data, but British government bonds underperformed as investors bet the BoE would delay following the lead of the European Central Bank, which cut rates earlier this month.
"Services CPI continues to print to the upside (which) we think removes any lingering risk that the Monetary Policy Committee might announce a cut to Bank Rate tomorrow," said Cathal Kennedy, senior UK economist at RBC Capital Markets.
The drop in annual consumer price inflation from April's 2.3% reading - in line with economists' expectations - took it to its lowest since July 2021 and marks a sharp decline from the 41-year high of 11.1% in October 2022.
The fall has been sharper than in the euro zone or the United States, where consumer price inflation in May was 2.6% and 3.3% respectively, belying concerns a year ago that British inflation was proving unusually sticky.
Inflation first began to pick up in most Western economies in the second half of 2021 due to bottlenecks from the COVID-19 pandemic, then surged after Russia's full-scale invasion of Ukraine in February 2022 caused natural gas prices to soar.
Consumer prices in Britain are up more than 20% over the past three years, squeezing living standards and contributing to the unpopularity of Sunak's Conservatives, who are around 20 points behind the opposition Labour Party in opinion polls.
Sunak said that the drop in inflation since he took over from his Conservative predecessor Liz Truss - whose fiscal policy triggered a surge in government borrowing costs - was evidence that his economic policies were working.
"Let's not put all that progress at risk with Labour," he added in a video clip.
Labour's Rachel Reeves, who looks set to be Britain's next finance minister after the election, said reelecting the Conservatives would bring "five more years of chaos."
NO EARLY RATE CUT
The BoE has said a return of inflation to its target is not enough on its own for it to start cutting interest rates.
"Rate-setters will still need to weigh the fall in headline inflation against signs that domestic price pressures, such as elevated pay growth, are proving slower to come down," Martin Sartorius, principal economist at the Confederation of British Industry, said.
Most economists in a Reuters poll last week thought the central bank would start to cut rates in August from their 16-year high of 5.25%, but financial markets see only a 30% chance of an August rate cut and think a first move is more likely in September or November.
Regular pay in the private sector in the three months to April grew by an annual 5.8%, down only slightly from the first quarter of this year and almost double the rate most BoE policymakers think is needed to keep inflation at 2%.
The most recent fall in inflation was partly driven by a cut in regulated household energy bills in April - the effect of which will fade later in the year, when the BoE forecasts inflation will rise to 2.6%.
Lower food prices were the biggest factor pushing inflation down in May, reducing the annual rate of inflation for food and non-alcoholic drinks to 1.7% from a 45-year high of 19.2% in March 2023.
Cheaper electrical appliances and a smaller rise in the cost of recreational and cultural activities also helped lower inflation.
Higher air fares were the biggest factor to cause services price inflation to fall less than expected. Air fares are volatile, and some economists view them as a poor guide to broader inflation trends.
(Reporting by David Milliken and Suban Abdulla; Editing by Kate Holton and Alexander Smith)