I am an MSc student working on PhD applications at the moment, and I'm in the field of molecular biology / biomedical science. I hope you can give me some advice on who to ask for my academic references, because I have a few options there.

As part of my current degree I have to do two research internships (half a year each).
During the first one I was supervised by a PhD student, who was quite happy with my work and writing, and I already know she would gladly write me a stellar reference. She's near the end of her own PhD but won't have the fancy title before I need the reference.
My second internship, which I'm right in the middle of, is supervised by a Postdoc who would probably agree to write me a reference as well.
In both cases, the PIs are full professors and I see them in weekly meetings and they've seen me present or briefly summarize results. But all in all, the PIs don't know me as well as the two above-mentioned daily supervisors.
Then there's another option... I have yet another supervisor (professor) for a literature review essay that I can write at my own pace. I've only had one meeting with him so far, but that could change - the application deadline is more than 2 months away (and I can basically pop in any time to discuss with my supervisor).

I should mention that all these people are affiliated with the same university hospital in different departments.

I can name 2 referees, so who should I ask? Is it better if my reference is from a professor, even if they may not know me as well? Or should I ask my internship supervisors instead? Only one internship and the literature review professor (i.e. some practical and some literature work)?

Ok lets chop it up (discuss it)

For the first reference, I'd go with the research internship PhD student (which you have completed). Why? Well as a PhD student they would be capable of wording your reference letter in a research oriented vernacular pleasing to the persons reviewing your PhD application. PhD title would be nice, but not a deal breaker in my opinion.

As for the second one, I think you should get a reference from BOTH the Post doc AND the literature review Prof. That way as you tailor your application according to how a particular university weighs certain skills, you can choose which one is more appropriate for said application.

Question: Have any of your MSc Lecturers / Professors moved on from your university to other posts elsewhere, be it academia or private sector / industry? If so you could get a reference from them and their current posting would reflect some diversity in your references if you are concerned about that.

Fled, most of the time you are not going to see the reference - it is going to go directly to the person requesting it so you can't make the choice between two.

Datura, I think you should get the references from the PIs rather than the postdoc or PhD student. The PIs will probably ask their opinion anyway and it will look better coming from them rather than a PhD student or PD I think.

Thanks you both for your opinions!

The references are indeed submitted directly, I only give the referees' contact details. Looking for someone who's moved to another institution is a good idea; I will see if that's possible (although I don't have high hopes).

My apologies, all of the academics whom have ever acted as references for me would email me a draft for my "approval", but I am not from the UK so I did not account for cultural differences :P Sounds like you have a plan and TreeofLife gave you excellent advice.