Every login must have a unique email address, so you cannot share them. Getting an email is free with many services.
Note that you can 'make a request for someone else', to learn how to do this please click here
If you have a gmail address, you can use the + character to create different addresses which come into the same inbox. For example, if your address is firstname.lastname@example.org you could register John with the email email@example.com and Mary with the email firstname.lastname@example.org. You will need to remember the extension when you log in to the askmyGP system, but will not need to make any changes to your email or inbox.