Many thanks for the suggestions, I'm not the btinternet customer my recipient is, and as she is still in the middle of post-funeral trauma I'm not inclined to bother her further at the moment.
After nearly 1 1/2 hours of being " a very important customer, thank you for waiting" my ISP's representative in some cave in Uttar Pradesh ( I think ) proved - to himself - that it wasn't their fault, and my problem most likely lay with Outlook, but "they" weren't trained to solve Outlook problems so go ask Microsoft.
Fat chance.