Sometimes diplomacy of the highest seriousness gives you moments of pure comedy, and Iraq’s offer yesterday to mediate between the US and Iran was one of those.

The Iraqi Government has achieved almost perfect impotence, with a malign gloss. It couldn’t stop the sectarian violence if it wanted to (although it appears to condone the bloody domination of the country by the Shia militias) and it can’t run the oil industry, the country’s most tangible asset.

All it can do is turn up to conferences, ask for more money and torment the US with the accusation that it has ruined the country and the request for US forces to stay. And it can throw in the kind of gesture that real governments would be embarrassed to make, such as yesterday’s offer to heal the 28-year breach in relations between the world’s superpower and the Middle East’s giant.

It didn’t have much luck with that either, as it happens. Although Condoleezza Rice, the US Secretary of State, and Manouchehr Mottaki, the Iranian Foreign Minister, “exchanged pleasantries” over lunch, the chances of a substantial US-Iranian meeting looked slim.

In theory, those talks sound useful, and it has become fashionable to recommend them. Iraq is right to argue – as did the Baker-Hamilton commission in the US – that it is impossible to have peace in Iraq without the support of Iran. Nicholas Burns, the US UnderSecretary of State for Political Affairs, made the point in London this week, saying that “Iran is playing a central role in the four great interconnected crises in the Middle East that are part of US foreign policy” – its nuclear work, its alleged role in supporting Iraq’s Shia militants, its opposition to Israel and its support of Hezbollah.

The US has often regarded the mere offer of contact as a reward for good behaviour, even if those punished by the withholding of contact (such as Cuba) sail blithely on. The attitude has been exasperating to British ministers even during the past ten years of great closeness to Washington.

British ministers are right generally to have taken the worldlier view that it is almost always worth talking to opponents. There are few situations that cannot be improved, if only by prodding at technical details, even though the fundamental disagreements remain.

But for the US to talk to Iran about Iraq may be one of those rare exceptions where it is hard to say what even technical talks would be about, as the two countries’ goals contradict each other. The US still hopes that Iraq can be a multi-ethnic democracy; Iran wants it to be a “managed democracy”, in that new euphemism, run by Shias for their benefit and for Tehran’s.

There are other questions that the US might usefully discuss with Iran, as Burns helpfully listed. But in Iraq, only if the US has reached the desperate point where it wants peace, regardless of the nature of the government, does it have something to discuss with Iran.

Britain has slid out of its role as “lead nation” in Afghanistan’s drugs battle but has hardly advertised the fact. In a written answer, in yesterday’s Hansard (and echoing an exchange in March), Margaret Beckett, the Foreign Secretary, told William Hague that “the UK took on lead G8 responsibility for counter-narcotics . . . in 2001”, but that “in 2006 it was agreed that the concept of ‘lead nation’ was redundant”. Afghanistan itself would take the lead; the UK would be merely its “partner nation”.

It may be worth bringing the shift to the attention of US officials, then. On March 1 General James Jones, who retired only weeks earlier, told the Senate Armed Services Committee that the UK, as the “lead nation” on Afghan drugs, “is failing in implementing a cohesive strategy to even begin to resolve a problem that will result in international failure in Afghanistan if not addressed”.

When roles were doled out in 2001, one Foreign Office official said: “We picked up the drugs card, and perhaps that wasn’t the best one.” Indeed. Britain has hoped to slip it back into the pack without anyone noticing.

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