Hello there!
We were recently approved for my partner to have a Common Law Visa.
In terms of proof of the relationship, we included:
-Tenancy Agreement stating both our names at our current address
-Tenancy Agreement showing just his name at our previous address, but mail from the UK Government (things like my National Insurance Number) addressed to me at the same address
-A letter from his dad saying we lived with him for the short weeks before moving to our own address in the UK
-Copies of cashed cheques (printed from my online bank account history) stating "Rent for ___sponsor___ and ___applicant___" in the Memo section of the cheque showing we lived together in Canada (we didn't have a tenancy agreement).
-(Although not required) The Statutory Declaration of Common Law Union, sworn before three magistrates.
-Joint bank account
-Two Statutory Declarations from my mother and his mother stating they are aware of our relationship, support it, and support our future plans together.
-Several (maybe 5) printed e-mails from friends (not notorised) stating how they know us (whether they met us apart or together) and that they know about us and support us.
-A few e-mails and Facebook messages that show our relationship growing and our communication regarding what we want out of our relationship (this was done while we were living apart when we were deciding whether I should move to the UK). We e-mailed about whether we want to continue our relationship and how we want to achieve it, then how we grow throughout our relationship after I move to the UK ("you doin' dishes tonight?", etc)
-Searched each other's names in our e-mail inboxes and printed the screen that shows the inbox with only each other's names to show just how much we communicate via e-mail even during the time we live together.
-Mobile Phone statements printed from the internet, with his phone number highlighted (he has a pay-as-you-go so no statements) but the phone number matched the one he put on his application (these statements were addressed to the address we share).
-An EXPIRED life insurance form stating my partner as the beneficiary (it was part of the employment package but obviously expired when I quit that job, which I stated in the application)
-A "Timeline of Our Relationship" which included events like, "Met here on this date, went out together here on this date, a collection of photos from the summer together and all the things we did, moved in together on this date, moved to the UK on this date, we lived here, then here, then here; we worked here, then here, then here, etc."
Every event had its own "Section" which included all the proof we could muster that that event took place. So we had a Table of Contents which showed what the event was, what proof we included, and what section to find it in (e.g. "Met at work on this date in Section 1" --> Go to Section One --> Includes Tax Returns, Tax Slips, Pay Slips, Bank Statements showing the same depositor, pictures from work, etc.)
Our (outland) application took 2 months and 3 weeks to be approved from start to finish.
Hope that helps.