(Adds details, arrival in Pakistan)

By Katherine Baldwin

LASHKAR GAH, Afghanistan, July 25 (Reuters) - Britain's foreign minister and Afghanistan's leader backed the Afghan government's efforts on Wednesday to root out deep corruption that is driving people to side with the Taliban.

Britain's David Miliband held talks with Afghan President Hamid Karzai in Kabul and later in Helmand with the southern province's governor and army chiefs.

Britain has 7,100 troops based in Afghanistan, mostly in the Taliban stronghold of Helmand.

Miliband later flew to Pakistan, where, in talks on Thursday, he will encourage President Pervez Musharraf's efforts to fight militants and target radical schools as well as reinforce vital cooperation with Britain on counter-terrorism.

Miliband chose Afghanistan and Pakistan for his first major foreign trip since becoming foreign secretary to highlight new Prime Minister Gordon Brown's determination to tackle terrorism and radicalisation.

Speaking to reporters at British military headquarters in Lashkar Gah, Miliband said he and Karzai had agreed that progress in Afghanistan depended "on change from the bottom up as well as the top down".

"No one needs to tell President Karzai that good government, clean government are absolutely essential to Afghanistan's future. He said that to us," Miliband said.

Frustration with Karzai's government over deteriorating security, corruption and crime is growing among Afghans.

British and American officials have been pressing Karzai to get tough on bribery rackets in central and local government and the judiciary that push people towards Taliban militants.

Violence has surged in the past 18 months, the bloodiest period since U.S.-led troops overthrew the Taliban government in 2001.

POROUS BORDERS

Karzai agreed he faced huge challenges to weed out corruption and especially to calm Afghanistan's lawless southern regions, which are being infiltrated by militants from Pakistan.

He has also recognised he has a huge task extending his government's remit, or some form of democratic accountability, to areas previously ruled by the Taliban or tribal leaders.

Miliband and Karzai met as the Pakistani army targeted militants on the Afghan-Pakistan border, a tribal area and hotbed of support for al Qaeda-linked militants, and as Karzai's government struggled with foreign hostage crises.

Miliband said the Taliban's shift from insurgency to terrorism tactics signalled weakness, not strength, although it raised fresh challenges.

British officials fear the consequences if NATO's mission in fighting the Taliban and al Qaeda-linked insurgents and efforts to extend government control to lawless areas fails.

"People go to the Taliban to avoid getting assassinated by the Taliban," said one British official based at Lashkar Gah.

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