Research proposal for PhD application - should I talk about my background?
While it may be institution/field/country-specific, from the description I assume that you are applying to the program and do not have a prospective advisor who has already agreed to supervise you, nor a project onto which you will be allocated. In this case, that seems similar to the American "statement of purpose" (SOP).

The first guideline is: follow the guidelines. They tell you exactly what they want to see in your statement. You should absolutely touch on all of those points.

In fact, many statements add nothing to the profile exactly because the applicants fail to understand its purpose. The only way that you will have the reader's attention is if you talk research. The statement should not be the place where you state everything that they could have read (in a more appropriate format) in the CV. Your background is, of course, relevant, and you should absolutely include it, but only as evidence of your motivation and involvement with the field and the tools that you wish to learn or use during your PhD. The key to a good statement is to seamlessly merge your interests, background, experience, fit and the necessary tools to accomplish your goal. You should leave a strong impression that you have a solid (not necessarily deep) understanding of the field you are getting into.

So, for instance, don't write this (parentheses are my comments):


  I have always liked to be boring and make people uncomfortable. Since
  I was a child, my parents would roll their eyes every time they read
  one of my essays. Rarely they would be able to finish. As I grey up, I
  felt the need to contaminate my friends with my excitement, and made
  them listen to incredibly long and meaningless talks. (Sorry to be
  blunt, but nobody cares about your childhood.) I graduate in May from
  Boring University and so far I have maintained a perfect GPA. In fact,
  I took several courses in how to be boring, such as Being Boring I and
  I have published a paper where we explored the mechanics of
  self-expression in boring situations, along with Dr. Cheeky Jokes. (I
  have your CV and your transcripts, I can see that.) Now, I want to
  further specialize in making people annoyed, and Awkward University's
  program in Social Engineering is certainly the best in the world (I
  know, why do you think I work here?) and will give me a strong
  background to make people uncomfortable while simultaneously being
  boring (nice, but what do you bring to the table?).


Rather, maybe you should word your essay like this (note how I touch on all three topics while simultaneously referencing the background and fit):


  The strong background that I acquired in boredom from Boring
  University has motivated me to further specialize in awkwardness.
  Working directly with Prof. Cheeky Jokes on the mechanics of
  self-expression in boring situations, I noticed that awkwardness
  emerges directly from personal interactions under these conditions.
  Under the supervision of Boring University's Ethical Review Board
  (ERB), we designed an empty room where we put people who knew each
  other but hadn't talked in several years. Upon examining the data, we
  found that they not only were extremely bored, but also engaged in
  very awkward conversations about their past and how their kids had
  grown up. This very exciting finding was later published in the
  Journal of Awkward Situations. Now, during my PhD and motivated by my
  previous research experience, I want to continue exploring the effect
  of boring situations in the emergence of awkwardness. During my
  research, I became interested in Prof. Clumsy's research on how to
  maximize awkwardness in daily situations. In fact, I believe that
  providing experimental validation for her recent work on finding the
  optimal number of people who will maximize awkwardness in a highschool
  reunion, which she modeled computationally, can be a major
  breakthrough in the field. While Prof. Clumsy has already disclosed
  that she is already working on that, I believe my experience with
  experimental social engineering can be a solid addition to her group,
  especially given that I have had thorough contact with ERBs.


Note, however, that in many cases the SOP is not heavily weighted in admissions, but that's probably field-dependent. And I am not in CS nor in the UK, so take my advice with a grain of salt.