I've now received replies back from both the DSA and the DVLA. Have a bottle of aspirin at hand.....

I took my third test today and you do sign a box stating that you have been resident in the UK for 185 days in the past year, so I guess the 6 month rule does apply...
Now that's rather curious, since according to the DSA they have no specific residency requirement for booking or taking the test!
Here's the response from the DSA:
I can confirm that there is no minimum residency period required before a candidate can apply to sit either their theory/hazard perception test or their practical test. However, there maybe a minimum residency period in order to gain a UK provisional licence.
The DSA are responsible for the monitoring of driving instructors and for conducting the driving test, and although we try to assist with all queries received, specific licence enquires need to be directed to the DVLA.
So as a provisional license is required in order to take the test, we turn to the DVLA. While waiting for a reply from Swansea, I did a little searching and found leaflet INF 38, "Driving in Great Britain (GB) as a visitor or a new resident."
http://www.dvla.gov.uk/media/pdf/leaflets/inf38.pdfThis suggests that the 185-day residency requirement applies
only to those arriving in Britain from another EU country:
If you want to take a GB driving test you must be normally resident in Great Britain. However, if you have moved to GB having recently been permanently resident in another state of the EC/EEA, you must have been normally resident in GB for 185 days in the 12 months prior to your application for a driving test and a full licence.
I can find nothing in that leaflet which suggests a similar mandatory period of residency for anyone coming directly to the U.K. from the U.S. (or any other non-EU/EEA country).
Now here's the e-mail from the DVLA in response to my query, complete with a whole load of superfluous information which is irrelevant to the questions I asked:
There is no explicit residency requirement appertaining to an applicant for a provisional licence. However, section 97(2) of the Road Traffic Act provides that 'if the application for the licence states that it is made for the purpose of enabling the applicant to drive a motor vehicle with a view to passing a rest of competence to drive, any licence granted in pursuance of the application shall be a provisional licence for that purpose'.
This means that applying for a provisional licence is intended to be no more than a means to an end i.e. the taking of a driving test. This implies that the applicant believes, anticipates or at least has a tenable hope that the applicant will ultimately take a test.
Anyone wishing to take a driving test in Great Britain must first comply with the residency requirements as defined in The Motor Vehicles (Driving Licences) Regulations. These requirements apply to all tests, including upgrades, and are defined in Regulation 38(1) as follows:
'...no person shall submit himself for a theory test or unitary test unless he satisfies the residence requirement specified in Section 89(1A) of the Road Traffic Act and where any question arises as to whether a person is normally resident in Great Britain or the United Kingdom (as the case may be) he shall be deemed to be normally resident there if he shows that he will have lived there for not less than 185 days during the period of 12 months ending on the day for which the test appointment is made'
The Motor Vehicles (Driving Licences) Regulations 1999 can be seen here, but regulation 38(1) is as quoted by DVLA:
http://www.opsi.gov.uk/si/si1999/uksi_19992864_en.pdfIt's about as clear as mud now, because the Road Traffic Act 1988 doesn't seem to contain any residency requirements in section 89(1)(a). Section 89(1)(c) contains a reference to being "normally resident," but only seems to apply to those with an exchangeable license.
http://www.opsi.gov.uk/acts/acts1988/ukpga_19880052_en_8#pt3-pb2-l1g89I haven't had time to trawl through the amendments to that 1988 Act, so there may well be something in those.
Anyway, we have DSA saying they have no minimum period of residency required for taking the test, and we have DVLA saying that there is no explicit requirement in order to apply for a provisional license, other than perhaps being "normally resident."
The driving license regulations they quote suggest that the 185-day rule might be applied only in cases where there is any doubt as to whether the person is resident or not. I guess that ties in with the INF38 leaflet about EU nationals, since they would not have visas etc. to prove residency.
So with the caveat that I'm no lawyer, as far as I can determine from what I've seen so far, if you have moved directly from the U.S. to the U.K. you may apply for a provisional license and take the test as soon as you wish, since there are no absolute time limits and -- I would presume -- your immigration status would indicate that you have become "normally resident."