It was a pied!!!
I ended up taking some toil and getting up on to the Wirral for around 3 o'clock. But by then the bird had moved off the sea wall and on to the roofs of the buildings near the boating club, and here it stayed for about 35 minutes, while the light faded.
The light wasn't great at this point, but that didn't matter as the bird flew right up to us and posed.
Pied wheatears spend their winters in eastern Africa (Sudan to Somalia south to north-east Tanzania) and south-west Arabia (Yemen). so its a long, long way from where it should be at this time of year.
The reason this is so controversial is that this practice of putting down artificial food has been blamed in the past for birds becoming too tame and complacent and then being predated.