I know that there is at least one person here who lived with her parents, didnt have a job and stayed for 6 months and didnt have any trouble at immigration, but everyone's experience is different.
She's talking about me. I'm a freelance writer, so I didn't have anything solid in terms of a job to return to.
When I went over, I took with me a print out from the front page of my internet banking (to show the balance as of the day I got on the plane), a copy of my most recent bank statement, a letter from my mom stating how much I paid her in rent and when she expected me back, and I had a letter from Tim (my boyfriend) outlining that he was providing me with room/board and he was a British Citizen, had a f/t job, owned his house, etc. he included his UK passport number, information about his employer, and how long he expected me to stay. The only thing the I/O told me he should have added to the letter was how long we had known each other. I also had in my folder print-outs of confirmations for show tickets we had to a play in Stratford a week after I arrived, a play in London a month into my visit,and a few other trips/events we planned to attend, but I was never asked for any of that. I know the I/O got a glimpse at my folder though and he could see it was full of information regarding my visit. The only thing I even needed to hand over was the letter from Tim, and I got my stamp and was done. No further questions, no questions about funds...I was pretty shocked, but I figured it also might have had to have something to do with my age (29 at the time) and how I was dressed (business casual).
I also only originally planned to stay for 2 months, got stamped in for 6, and then Tim and I decided we wanted me to stay longer due to a family emergency and the fact that we were enjoying our time together. I wound up staying longer than even we originally decided to extend my stay for (it started as stay until mid-January for his Uncle's funeral, then his Gran went into hospital and he wanted me to stay longer), but I made sure I left before the 6 months expired on my passport stamp.
Tim mailed me the letter to give to the I/O so I would have an envelope with a UK post mark and his signature in ink. He was going to fax/email it, but then he decided it was better if I had it postmarked.
But this might not work for you in your situation, so I wouldn't assume you'd get in just because you take along the same information. A girl in her early 20s came through LHR about a week after me and had the same types of documents I had and was planning on staying with her bf for 2 months and she was turned away, so YMMV.