I get 2 phones delivered every 12 or 18 months. Sometimes my wife signs for it or one of my boys. They never have to show any ID as your home is the ID. My youngest when he was 18 had to show proof of age as he looked only 14, he is a leap year baby too lol, he is 21 soon and still looks about 16. Under 18 cannot sign for anything but if older than 18 and look young, tell them to have ID with age.
Contact EE and tell them the problem of the passport and ask for it to be delivered, if asking nicely they should not charge you postage. I always at the beginning tell the customer support person that I love their accent, where do they come from, they laugh and next I get all the small things like postage free, I have even been given £5 credit. It works with male or female, we all like being liked.
Don't make things harder than what they are, just ask for it to be delivered, don't go into the story of your flatmate being only one in etc, that's between you and the delivery service. It really is easy...Bishop
