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The talks come at the start of Zardari's three-day trip to Europe where he is expected to call for greater help from the West in securing its border with Afghanistan.
Zardari is also appealing for western aid promises to be met - the international community pledged $5.7 billion of funding earlier this year but according to some reports only $300 million has been received.
Equally, Brown faces a delicate balancing act as he seeks to maintain Britain's ties with Pakistan while pressuring Zardari to accept US demands for more action against the Taliban.
Western leaders have tried to persuade Islamabad that it is the Taliban that is its enemy, not India.