After checking all the smoke alarms, I finally tracked the noise down to the electronic timer on the oven. We'd obviously had a power outage during the day, and the silly thing simply refused to reset itself. No matter how many buttons were twiddled, it continued to buzz. You can imagine the stress it put on the dog's ears! (Not to mention mine.)
Over five hours later, I'd finally located the old instruction book, which recommended pulling out a fuse from the outside electrical box for ten minutes.
Success. The silence is golden. Or is it? To tell the truth, the lack of buzz has now left me feeling rather nauseous, and emotionally fragile. It's worse than Chinese water torture!