Whether or should I ask for a reference from my advisor who I believe does not like me? I have good reason to believe that my academic advisor does not like me. However, I will need a reference if I am going to apply for graduate study. 

What can I do now? I got an excellent mark in my dissertation (I do not know if she marked it, or how exactly it works here in the UK), but I am pretty certain she does not like me very much. Assuming my judgment is correct, what would be the best course of action? Shall I risk asking her for a reference and hope she will be fair, or rather ask somebody else?
While I don't doubt your judgement of the situation, I think it's best if you put your doubts to one side.

Let's consider the best case scenario: you contact your adviser and they agree to write a strong reference letter for you, based on your excellent performance over the course of your dissertation. Great!

Now let's consider the worst case scenario: you contact your adviser and they refuse to write you a reference. What then are your alternatives? I would suggest contacting your personal tutor from university, or another lecturer who you knew well and have fewer doubts about their attitude towards you. As a last resort, you could ask someone in your place of work e.g. supervisor, line manager. Explain to them that the letter needs to emphasise your potential to succeed in graduate studies.

Finally, let's consider the most likely scenario: you contact your adviser and they agree to write you a reference. They remember that your working relationship was not the most positive, and this may be reflected in the tone of the letter. However, after six months or a year, this impression may have faded. The excellent grade in your dissertation, however, is concrete evidence of your ability to achieve, and they base their letter on this. The reference may not be glowing but it will be an accurate reflection of your potential.



As an aside, I would hope for your sake that your adviser is able to put their professional judgement of you above their personal feelings. Good luck!