What documentation do I need to provide at Bluport Immigration for my TM28 when renting from my girlfriend?

Some advice please. I hope this is the correct forum for asking.

I will soon be moving into a property rented by my girlfriend. The lease is in her name. Any idea what documentation I will require when I attend Bluport Immigration with my TM28?

I am assuming copies of the photo page of my passport, my original O-A visa, my current extension for the purposes of retirement, TM6, my last entry stamp and a copy of the rental agreement in my girlfriend's name.

However, that doesn't exactly prove I am living there, so how do I do that? I do have a telephone bill in my name at that address, is that of any use.

Thanks in anticipation.