Anokdale – I would keep a copy of the wedding invitation and hotel booking confirmation with the passports. they may ask for that.
If your mate has an Israeli id/passport , it could help to get a letter of a few lines from him about your visit, quoting that id..
Clearly none of that is essential and even without any of it, just be prepared for some extra questions. probably most intensly on the way out. If you don’t fly elal you shouldnt have any problems on the uk side.
Also, and i think this is probably obvious when dealing with all state officials -although I’ve often been amazed to hear that apparantly its not- avoid sarcasm /be straighforward when answering.
Have fun! – Tel Aviv is a great city!