How long ago did you visit TLV? I went last year and they no longer stamp passports, instead they scan the passport and give you a credit-card-sized piece of paper that has the passport scan and the date of entry and the validation period. (I also went the year before that, and they did stamp passports.)

Perhaps you want to end in TLV? It's one of the longer ex-LHR flights on BA that's still within the continent.