1. Even if there is no written tenancy agreement, there will be a tenancy in place - albeit verbal & therefore with terms which are difficult to determine. However, paying the rent is bound to be an essential term so you are right not to want to leave this. I've known of a landlord who didn't chase up unpaid rent for nearly a year & then demanded the lot in one go!
2. If Bednobs suggestion doesn't bear fruit you could do a land registry search (use the gov.uk site - not one of the expensive co.uk ones) to try & find the landlord's name & address.
3. You probably realise now that it's not a good idea to keep this sort of information on just one small device which can get lost/stolen - always best to keep it in paper form as a back-up to a computer or phone.