Thanks, everyone. Several have remarked that this is a silly, irritating game and I have to agree. Maybe I am naïve but I don’t normally haggle; if the initial price offer (of anything, not just breakdown cover) doesn’t suit I go elsewhere. But taking advice here I had an entertaining session on the phone this afternoon with the AA, the result of which was that they reduced the price by £86. That’ll do nicely.
And on the question of the tactics of the game, the “Press 2” option was “if you want to leave us”. That resulted in 15 minutes of waiting and I eventually rang off with the distinct impression that they were ignoring me. I called back straight away and pressed option 1 “if you want to re-new” and, like magic, I was answered immediately. Funny, that…