* Shareholder climate resolution rejected

* CEO warns UK windfall tax could impact future investments

LONDON, May 12 (Reuters) - BP shareholders on Thursday backed the energy company's climate strategy, while fewer investors than last year supported a resolution filed by an activist group urging faster action to battle climate change.

The vote at BP's annual general meeting came as the British government faced growing pressure to hit BP and its rivals with a windfall tax after energy companies posted a surge in profits on the back of rocketing oil and gas prices in recent weeks.

BP's chief executive, Bernard Looney, told the meeting that a windfall tax would not change the company's 18 billion pound ($22 billion) investment plans in Britain to 2030, though fiscal instability would be disruptive in the longer term.

BP's energy transition strategy includes cutting greenhouse gas emissions from the production and sale of oil, gas and other products to net zero by 2050, with a number of short- and medium-term targets.

The London-based company also plans to slash its oil and gas output by 40% and boost its renewable power business by 20-fold by 2030.

The non-binding resolution on Looney's climate strategy won the backing of 88.53% of shareholders, according to official results.

BP's climate targets are "relatively ambitious," but "further disclosures and a strengthening of targets will be required to convince most investors that its strategy is consistent" with U.N.-backed targets of limiting global warming to 1.5 degrees Celsius above pre-industrial levels, Bruce Duguid, head of stewardship at investment firm Hermes EOS, said at the meeting.

A resolution filed by the activist shareholder group Follow This that urged BP to set "inspirational" emission reduction targets, and which was opposed by the company's board, won the support of 14.86% of shareholders.

That was below the 20.6% support last year for a similar resolution filed by Follow This.

"Investors' short-termism, fueled by the current windfall profits of BP, might have prevailed over the medium-term risk of value destruction caused by the climate crisis,” Follow This founder Mark van Baal said in a statement.

(Reporting by Shadia Nasralla and Ron Bousso; editing by David Evans and Leslie Adler)