British soldiers must be feeling a little dizzy. Gordon Brown has made some big promises to them about troop numbers in Iraq, which have invariably proved inaccurate. Remember the 1,000 troops home for Christmas? And the halving of British troops serving in Iraq to 2,500 by the Spring? Ministers have either done some creative work on definitions of “home” or blamed changing conditions on the ground. But, from what I have been told, it has as much to do with the prime minister’s penchant for round numbers.

Mr Brown’s role in the “1,000 home for Christmas” has been well reported. The catchy announcement was made without consulting the Ministry of Defence. There was then a scramble to work out how the pledge could be met. In the end, about 500 support troops sent to Kuwait were defined as being out of Iraq and therefore “home”.

Mr Brown’s role in the setting the 2,500 target for the draw down in Iraq is less well known. Again, he delivered a catchy message (this time in the Commons in October): the British presence in Iraq would be halved by the Spring. The number was chosen “after detailed discussions with our military commanders, a meeting of the National Security Committee, [and] discussions with the Iraqi Government and our allies”, according to Mr Brown.

But since then, British officers have concluded there must be at least 2,800 men to be able to protect the base adequately. So even when the withdrawal resumes, we are unlikely to hit the magic 2,500 number. The rounding error had more to do with Downing St than inaccurate military plans, according to one defence insider. Another official suggested to me that the low number risked upsetting officials in the US and losing Britain any benefits, in terms of the special relationship, it has derived from taking part in the war. “They can be rather unforgiving”, the official said.

There is a startling statement buried near the end of this NY Times report about Nuri al-Maliki’s ill fated offensive in Basra:

the Iraqis did not trust the British and were not including them in their planning, according to a senior American officer.

From what British officials tell me, the lack of trust is mutual (and that is putting it politely).

Of all the presidential candidates, John McCain certainly has the biggest differences with Gordon Brown over how to handle Basra. Over at the Spectator Coffee House, James Forsyth has picked up some “straight talk” on British efforts to bring order to Iraq’s second biggest city. McCain says the British failed to counter the Iranians as they “moved into Southern Iraq”. “These are the penalties we continue to pay for the very bad mishandling of the war for nearly four years while they became solidly entrenched,” he added.

This reminded me of some of McCain’s more explicit criticisms of the British withdrawal plans. In February, he told reporters that he “did not think it was a good idea” for the British to draw down troops last year.

He softened the blow at the time with some warm remarks about the British commitment. (”I understand the British domestic situation and I very much appreciate the service and sacrifice the British military made in Iraq…Obviously we’d have liked to see them stay longer but the enormous contribution they made in Iraq and Afghanistan I have to just be grateful for.”)

But I expect this would have given little comfort to British officials wary of his ambitions in Iraq should he be elected president.  Would McCain request that the British take part in a Basra “surge”? And would he embarrass Gordon Brown by sending US troops to Basra if the prime minister said no?