Apologies for not reporting the outcome of my relatives abortive sortie to Heathrow on Saturday - I have had to wait until the tears stopped flowing.....
They duly rolled up to a fairly empty Terminal 5, where they were very quickly assisted by very friendly courteous and polite BA staff, including a senior supervisor, who tried valiantly by telephone to persuade the resident US Homeland Security team that they should be allowed to travel, but to no avail. The Homeland Security team did, however, take the trouble to pass on via the BA supervisor a preferred email contact in the US Embassy to whom they said formal application should be made for a visa waiver or a National Interest Exception (NIE) in the hope that that approach might prove more fruitful.
They apparently struck whilst the iron was hot by submitting such an application on Sunday, but have now heard through a genuinely fairly personal and courteous email that they regrettably still do not come up to the bar, which is quite interesting since I had felt that they had a reasonably strong case. The Embassy email also contained some advice on how travel from the UK to the US through a third country might be possible under certain fairly stringent conditions, but perfectly understandably equally took great care to point out that they could not comment in any way on the means or feasibility of doing so.
The couple concerned completely respect the decision, although frankly and understandably regretful that they might have saved themselves some heartache - and money! - if they had submitted their evidence well in advance but, to be fair, some of the more telling medical evidence was of very recent origin. In accepting the outcome, they can at least comfort themselves that they would not have been allowed to travel whether before or after any application and, as they said themselves, they had nothing better to do on Saturday!
The good news, if any, is slightly ironic in that they have both been advised virtually simultaneously that they have been conditionally approved for Global Entry enrollment, with the added bonus that the necessary interview for full approval can now be conducted through the Enrollment on Arrival, scheme, now available at a fairly extensive list of US airports and of course Dublin and Shannon. Regrettably, no response was received as to whether they could or should reapply for a new ESTA.....
In summary, the original ESTA emails were indeed kosher, the bar for the award of a visa waiver or an NIE is and remains very high but, like so many things in life, it can be worth a try.
With grateful thanks for all the helpful and interesting input, some of which such as Hartington's is pretty accurate - and I also had to smile at the input from someone with the moniker "Farci" - my relatives were also stuffed....
Jack