Jessielee -
If your "2 years living together" isn't straightforward (in other words, you can't give them EXACTLY what they ask for on the application form), you might be better off applying by post rather than in person.
I was in a similar situation to you - spent one year living with my partner "on & off" via visits, etc. and then one whole year living with him. I spoke to a couple of immigration lawyers, both of whom suggested I should apply by post.
Apparently, when you apply in person if your application isn't immediately "straightforward" they are more likely to either reject it immediately or send it off for futher processing (meaning you've just wasted the extra 100pounds you paid for an in person application). Whereas if you send it by post, not only is it cheaper but apparently they are more likely to look at it in more detail.
To answer your question: The application form (Form FLR(M)) states that they need to see something like 5 documents addressed to you both at the same address for each year, or 4 documents addressed to one person and 2 documents addressed to the other at the same address for each year (I'm not sure I've got the number of documents exactly right, I'm too lazy to check). You can find the application form on the IND website (
http://ind.homeoffice.gov.uk)
If you don't have the above, send in ANYTHING that shows the two of you were together, and in a relationship akin to marriage. When I applied, I submitted the 5 or so documents addressed to us both at the same address for the second year. For the first year, I didn't have anything like this. So instead I showed plane tickets, phone bills, photos of us together etc along with statements from friends and family that we were in a relationship akin to marriage at this time (send me a private message if you want the full list of everything I sent, I have it saved on my computer somewhere).
Have a read of both the Immigration Rules and the IDI's (Immigration Directorate's Instructions) for this category. They give you an excellent idea of what the IND is looking for. They can be found at
http://ind.homeoffice.gov.uk in the "Law & Policy" section.
Hope this helps!
-Sara.