UPDATE 2-Shares in UK outsourcer Capita slump again on weak results

* Shares down 40 pct in past year

* Underlying revenue falls 3 pct in H1

* Capita still looking for a new CEO (Writes through, adds reaction)

LONDON, Sept 21 (Reuters) - Shares in Capita tumbled 10 percent on Thursday as the British outsourcer reported weak first-half results, a disappointing outlook and no progress in its hunt for a chief executive.

Capita, which provides IT-led services for companies looking to cut costs, has issued a string of profit warnings following a slowdown from clients and problems with badly-run contracts, sending its shares down 40 percent over the past year.

On Thursday it said its first-half underlying revenue declined by 3 percent as it worked its way through difficult contracts.

The company, one of Britain's biggest employers with more than 70,000 staff, said it expects pretax profit before significant new contracts and restructuring to rise modestly in the second half, compared to the first half of 2017. Analysts at Stifel said that implied a mid-single-digit cut to forecasts.

"We remain confident that the actions we commenced last year are making Capita a simpler business, well positioned for the future under new leadership," it said.

The company said it was still looking for a new CEO to replace Andy Parker, who was at the helm for three years and left the company this month. "The board is pleased with progress in our search process for a successor," it said.

Capita, which generates revenues of more than 4 billion pounds a year, operates in over a dozen business sectors from health to retail to transport. Services span administration processing such as call centres, TV licences for the BBC and recruitment.

The company is trying to simplify its structure after years of acquisition-led growth and a structure which many analysts say has become difficult to manage.

Its clients, split roughly evenly between public and private sectors, have slowed the pace of their spending following last year's Brexit vote.

"A disappointing set of numbers in our view likely to lead to some modest earnings downgrades," Stifel said. UBS said that a lack of guidance on the outlook beyond 2017 may have spooked investors.

Capita's problems are reflected in its peer group as business services face slower growth as clients become more demanding on budgets and more reluctant to spend heavily. ($1 = 0.7408 pounds) (Writing by Kate Holton and Paul Sandle; Editing by Susan Fenton)