A popular cartoon in Punch magazine at the end of the First World War showed President Woodrow Wilson, founder of the League of Nations, stepping over the Atlantic Ocean in order to attend the Versailles peace conference. "Now to get back to a continent where I'm appreciated," he says, crossly.

Wilson fell victim to an obsessive conviction that his own country was too small for his talents, and only a world stage would do. Britain's Prime Minister may be making the same mistake as he hurtles round the globe on his various missions. One day it's Brussels and then Afghanistan, India and Pakistan. Fine-sounding but banal sentiments are expressed but the ultimate point of these missions remains elusive.

True, no one can object to the Prime Minister making a pre-Christmas visit to hard-pressed troops in Afghanistan after Friday's tragic deaths of four soldiers. But what purpose does Mr Brown think he is serving in India and Pakistan, where the lightest word on one side of the border can so easily be taken the wrong way on the other?

Relations between these two countries are now more combustible than they have been for years, since the Mumbai bombings in which more than 170 died and in which Pakistan-born militants have been implicated. Those behind the bombings have succeeded in their principal goals: to fan the flame of confessional hatred, undermine two fragile governments; halt tentative moves towards reconciliation between neighbours, and end hopes of a peaceful dialogue over Kashmir. But given that those same Islamist militants detest – and work for the overthrow of – Pakistan's pro-Western government, it is crass of Mr Brown to proclaim – from India of all places – that he supports more pressure on Islamabad, and then, flying on to Pakistan, wag his finger at the President and say Britain seeks a direct role in interrogating suspected extremists on Pakistan's soil.

While we must assume Mr Brown has no desire to undermine President Zardari's shaky grip on affairs, this clumsy intervention has done just that. Benazir Bhutto's widower is already damned in the eyes of a large percentage of Pakistan's population as a Western lackey. Now Mr Brown has confirmed him in that role. Mr Brown has every right to draw the attention of the Pakistan government to the fact that the there is a Pakistan "dimension" to both the 2005 bombings in London and to other planned Islamist militant attacks in the UK. But it is wrong of Mr Brown to seem to heap blame on the authorities in Islamabad for a phenomenon of militancy that poses far more of a threat to them than us. The issue of religious extremism ought to be addressed purely bilaterally, between London and Islamabad, not as part of some wider British mediating mission between India and Pakistan.

Finally the British public is entitled to wonder whether this globetrotting by Mr Brown is timely, and whether, when so many people are losing their jobs, he might not be better off at his desk, addressing the growing number of critics of the economical revival plans, instead of adding his two pence to various international crises in which Britain cannot seriously do anything useful.

The record of national leaders who become over-enamoured of the world stage is not good. After presiding over the Peace of Versailles and the creation of the League of Nations, US voters punished Wilson's Democrats. Churchill, another leader more at home on the world stage than in Britain, was poorly rewarded by voters in 1945. Mr Brown might like to ponder their fates before busily filling in his travel diary for 2009.