Questions on Unmarried partner application

Hey everyone, I'm new to this site, so I apologize if these questions have already been asked but some of these I haven't been able to find answers for.

My girlfriend is a British citizen who has been living in Canada for the past several years. We have been together for about 3 years and living together for about 2 and a half years. We have decided to move to the UK and she has already left to get a job set up in order to (hopefully) make it easier for me to get over there.

Now, we have several supporting documents, however many of our bills and such things were kept in only one of our names rather than both. We do however, have a couple of tax documents from the government of Canada stating that we are a common law couple due to living together for at least two years which should help our cause. Any suggestions on whether or not this will actually help?

Also, we have a letter from her parents stating that it is fine if we move in with them, as well as a rental agreement we signed with them to rent one of their bedrooms. Also a copy of the deed stating that they do, in fact own the house.

My question is is this enough for supporting documents, or do we need more than this? We have about $35,000 saved between the two of us ad both currently have jobs (one in the UK)... does anyone forsee any problems here?