* British Gas boss Weston to join Aggreko as CEO
* Centrica "looking rudderless", says analyst
* Weston subject to 12-month notice period at Centrica
* Aggreko shares down 5 pct (Writes through, adds detail, analyst comment, Aggreko impact)
LONDON, May 29 (Reuters) - The head of Centrica's British Gas division is leaving the company, it said on Thursday, joining other high-profile departures that leave a leadership vacuum as the group contends with public and political anger over soaring energy bills.
The loss of Chris Weston follows the announcement in January that Finance Director Nick Luff is to leave Centrica this year and comes at the same time as the British group's board makes preparations for the expected exit of long-serving CEO Sam Laidlaw.
"Centrica is looking rudderless. This is dangerous in a world of increasingly choppy waters," Deutsche Bank equity analyst Martin Brough said.
The group's share price was undamaged by Thursday's news - trading almost 2 percent higher at 337.4 pence by 1327 GMT - but analysts said that its valuation could suffer if the leadership problems are not ironed out quickly.
Brough said the difference between a well-managed and trusted British Gas business and a failing one could be as much as 100 pence per share, nearly a third of the current price.
Weston is leaving to take the helm at Aggreko, the world's biggest provider of temporary power, which now faces its own leadership void because its new recruit is subject to a 12-month notice period at Centrica.
Aggreko has been without a chief executive since Rupert Soames left to lead support services company Serco this year. Angus Cockburn, formerly Aggreko's finance director, was appointed to run the business as interim CEO, but he will be leaving the company later in the year, with some media reports suggesting he may join Soames at Serco.
A further announcement on the timing of Weston's departure will be made in due course, Centrica said. But that leaves Aggreko facing the possibility of being without a CEO for five months if Cockburn leaves at the end of this year.
Analysts at Liberum said Cockburn's departure is a significant loss for Aggreko, while others questioned Weston's lack of leadership experience. The company's shares were down more than 5 percent by 1355 GMT.
An Aggreko spokesman said the company would make appropriate arrangements if Weston's notice period leaves it without an interim CEO.
Aggreko said it had chosen Weston because of his wide experience at Centrica, where he is responsible for operations at both British Gas and Direct Energy in the United States, with combined revenue of 22 billion pounds ($36.75 billion), profit of 1.3 billion pounds and more than 35,000 employees.
Centrica chief Laidlaw, meanwhile, is expected to announce his exit soon. He has been in charge at the company since 2006, but his departure is widely expected after the board said this month that it was looking at succession options.
Sky News reported late on Wednesday that Laidlaw is set to be replaced by Iain Conn, a senior BP executive.
"Centrica need to admit Sam Laidlaw is leaving and announce a new CEO as soon as possible to avoid leaving a bigger void," said John Musk, managing director of utilities equity research at RBC Capital Markets.
The leadership crisis comes as Britain's largest energy supplier faces huge political pressure over steep rises in bills that have squeezed household incomes.
Opposition leader Ed Miliband has promised a temporary freeze on energy bills if his party is elected in next year. British Gas and its peers also face an regulatory investigation over energy competition that could lead to the division's separation from Centrica.
Centrica's profits have been hit hard by weak domestic demand and loss-making power stations. It has blamed increases to energy tariffs on rising commodity prices and the government's green energy levies. ($1 = 0.5986 British Pounds)
(Additional reporting by Li-mei Hoang and Neil Maidment; Editing by David Goodman)