A truth rarely acknowledged in the recent history of British-US relations is that the care either side lavishes on preparations for a leader's visit tends to be in inverse proportion to the warmth of the relationship. That it is the appearance, rather than the substance, of the Prime Minister's trip to Washington which has been front and central in recent days speaks volumes about the personal distance that remains between Barack Obama and David Cameron.

Thus, much is made of the fact that Mr Cameron will be accompanied by his wife; that her programme includes a nod to the London Olympics; that girls from the school Mrs Obama visited in London are in the Camerons' party, and that Mr Cameron will have the honour of accompanying the US President on Air Force One to a college basketball game in Dayton, Ohio – Dayton being the venue for the 1995 talks that ended the Bosnia conflict, and Ohio a swing state key to Mr Obama's re-election chances.

Given the havoc wreaked by the extra-special relationship between Tony Blair and George Bush, however, it may be no bad thing for British-US relations to be going through a cooler, less personal, phase. Nor should it be seen as catastrophic if pretensions to specialness (on London's side) are allowed to fade. For two countries of such disparate size, wealth and power, national interests are bound to differ.

And if the much-touted fripperies of this visit are stripped away, there is much unfinished business of an eminently serious nature to be conducted. Afghanistan would always have loomed large in Mr Cameron's Oval Office talks, even without the Kandahar shootings at the weekend. Not only is this engagement the biggest and most costly manifestation of British-US military co-operation, now that the Iraq war is in the past, but much planning and co-ordination is needed if Mr Obama is to honour his pledge to end the US combat role by late 2014.

The murders of 16 Afghan civilians, including nine children, by a US serviceman, however, make a difficult situation infinitely worse. Just since the beginning of the year, there has been the videoclip of US Marines urinating on the bodies of three presumed Taliban fighters; a US air strike that killed eight young Afghans in error; and the discovery that copies of the Koran were burnt at the Bagram airbase. The climate was hardly conducive to a measured and orderly departure. The deaths of six British soldiers last week – the largest single UK loss since 2006 – encouraged calls in Britain, including from this newspaper, for the withdrawal to be accelerated.

As leaders of the countries with the most troops in Afghanistan, Mr Cameron and Mr Obama would have ample material for their discussions. But the Afghan engagement is but one of many issues clamouring for attention. Inseparable from the future of Afghanistan are relations with Pakistan, as well as the progress of talks – in Qatar – with the Taliban.

Then there is what to do about Syria, and whether to help the opposition. Mr Obama will surely want to know how post-Gaddafi Libya is faring, while Mr Cameron will want to be kept abreast of US thinking about possible military intervention to frustrate Iran's nuclear ambitions. And if this were not enough, there is a Nato summit in two months' time in Chicago – another electioneering opportunity for Mr Obama – at which the future of the alliance, and such delicate issues as missile defence and relations with Russia and China, will be in the frame.

At a time when there is so much for two old allies to decide, it should be a matter for relief on both sides of the Atlantic that it is professional, rather than personal, considerations that will be paramount.