Sorry to be posting this again but I'm still stuck and hope that a fresh
pair of eyes might spot this and be able to help. I've added the latest
developments at the bottom.

Having bought a second-hand Accord Executive (UK, 2001 automatic 2ltr)
> we thought it prudent to order a new key from our local Honda
> dealership, as there was only one key supplied with the car. The key
> was obtained from Honda UK and programmed by the dealership, however,
> it refused to start the engine. Honda UK was consulted and they
> suggested that the engine control module was faulty, and the
> dealership swapped in another ECM but the problem persisted. The
> Dealer then obtained another key from Honda, but this one also refuses
> to work. The Dealer now says they cannot afford to investigate further
> and have (reluctantly) returned the £40+ that I had paid for the
> "blank" key. We are now back to square one, and worried as to what we
> could do if our only key failed or was lost. Grateful for any
> observations. Wayne.

Since I posted the original plea, a couple of things have happened , though.
nothing that helps.

I obtained a second original key from the previous owner. The fob works
fine, but that key also won't start the engine.
I returned the car to the Honda dealership it came from, (a 240 mile round
trip), they tried to program the key but also failed. They couldn't offer
much other help.
I contacted Honda Customer Services who could offer no help at all!, apart
from telling me to go back to the dealer. Isn't technology wonderful.......