Interline is definitely the way to go. If your wife cannot get them to interline it will be a bit more of a fuss, but not too bad.
Officially, BA will not let her check the bags in until 3 hours before the flight. However when flying in premium cabins, or as an elite travelling in coach, I have had them take my bag much earlier than that, so if she is an elite or booked at the good end of the plane it's worth a try.
If they won't take the bag, there is a secure luggage store in Heathrow Terminal 4 (which is the terminal the Tel Aviv flight leaves from). They charge 6 pounds per bag per day (or part thereof), so quite reasonable.