There are two things you need to focus on in a common-law sponsorship. The first is proving that you actually qualify as common-law partners. In order to do this you need to show that you've "co-habitated", in a conjugal relationship, for at least one continuous year. There is information in Section 5.25 of the
OP2 Processing Manuals that defines a conjugal relationship. There is information in Sections 5.35 of the same manual that lists things that will help prove cohabitation.
The second thing you have to do is demonstrate that yours is a genuine relationship - not one entered into in order to facilitate the entry of your foreign national partner to Canada. This is where things like photos, emails, cards and letters, trips to visit one another, etc., factor in. What I did, in response to the questions in the Spouse/Common-law Partner Questionairre, was use photos to substantiate all the important dates in our relationship. I also provided phone records to illustrate our contact when we weren't together, and I provided proof of all of our trips to visit each other. I didn't include emails because, frankly, we didn't have any - we spent hours everyday on the phone or on chat, but it wasn't possible back then to save chat conversations so we didn't have those either. I think what spoke most strongly for us was the number of trips we made to see one another (14 in 16 months), the amount of time we spent on the phone together, and the length of our relationship (3.5 years prior to marriage). So, the fact that you've been living together in the UK will speak to the genuine nature of your relationship, but in addition you should be able to demonstrate the development of your relationship prior to moving in together and the continuing nature of your relationship, even if you aren't able to continue living together when you have to return to Canada. That can be through select emails/chats/phone records, photos, etc., but you don't need to inundate them in order to illustrate what you need to. Quality over quantity.