I did some further tinkering and found a solution myself, very close to that suggested by garysgold. For anyone interested, here it is.
Control Panel/Default Programs/Set program access and computer defaults. "Custom" had the dot. I expanded this option and dotted "Mozilla Thunderbird" (leaving the dot at "Use my current e-mail program" will not do). Then clicked "OK" and all was well.
(Bizarrely, when I return to this, the last-mentioned dot has returned to "Use my current e-mail program" but the function remains available.)