YA 1960's/70's last man on earth book

Hi, all. As an adolescent in the early 1970's, I read a book about the last man on earth (I think the title may have been something like that, but it was neither the Isaac Asimov short story collection), with an image of a hot air balloon on the cover. First most of the world is wiped out, then a small group of children and the inventor scrounge around to survive, and ultimately, I believe most die. I believe it was by a British author. I can't for the life of me find it or recall the name, and it feels really relevant right now. Can anyone help me locate it? Thank you.
post-apocalyptic

A friend found the answer: The Last Man Alive, by A.S. Neill

Touchstone: The Last Man Alive