By Jonathan Marcus
BBC diplomatic correspondent
Mr Zardari is on a private visit to Britain
Pakistani President Asif Ali Zardari has met British PM Gordon Brown on a private visit to Britain.
Their talks come at a crucial moment with a spike in attacks in Afghanistan from Pakistan-based Taleban fighters.
There is also a growing rift between Washington and Islamabad on US cross-border operations.
There is rising concern in Pakistan over unilateral US military action - there have been some five US attacks into Pakistan in the last two weeks.
The fate of Pakistan's democracy matters to Britain, not just because of the increasingly costly war in Afghanistan but also because of the potential reverberations of that conflict on the streets of Britain itself.
Thus the timing of this encounter between Mr Zardari and Mr Brown is critical.
There have been some five US attacks into Pakistan in the last 10 days or so. On Monday, there were reports that another US helicopter-borne incursion from Afghanistan was forced to turn back after coming under fire from Pakistani troops.
It is no exaggeration to say that there is a developing crisis in ties between Pakistan and the United States.
And Britain, as America's closest military ally in Afghanistan, is caught in the middle.
The British government has noticeably refused to condemn the US incursions.
The problem is that the growing level of violence in Afghanistan is making Taleban supply bases and training camps in Pakistan much more important targets.
US policy has shifted. And pre-existing agreements between Pakistan and the US military on the scope of cross-border operations - the use of drones for example rather than boots on the ground - seem, in the words of one insider, to have become "frayed".
Civilian casualties, too, have inevitably inflamed passions.
Mr Brown may well tell his guest that Pakistan's own military must do more and that co-ordination between Pakistan and Afghanistan must be stepped up.
But neither Britain nor Pakistan seem to have much say in determining the parameters of the Pentagon's operations.