Hard to say, those predicted grades wouldn't be so hard to attain I imagine for you. Depending on what the requirements for physics are at Kings (AAA in the prospectus) I can imagine it would be quite tough applying here. Of course, that's only the grade aspect, depends on the rest of your application (Which I'll take your word is awesome!
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I wouldn't be able to shed further light on an interview I'm afraid. Only says in the prospectus that they may interview some people, but in this thread I think you've seen some folks applying for Neuro get an off just like that. As you mentioned too, you're a mature student. Do you have another degree behind you in the past?
In terms of an access diploma, it shouldn't hurt your chances at all. From the prospectus this is stated as the requirement for entry. Does this apply for you?
Access to HE Diploma Access to Science (or similar) with 45 Level 3 credits: 33 must be from units awarded at Distinction, with the remaining Level 3 credits at Merit. Level 3 study must include Chemistry and Biology. Level 3 study of Maths or Physics also preferred.
You predictions are on point with the entry requirement. As for what the most likely scenario is, I can't say sadly. It says that not everyone is interviewed, and not everyone who gets an offer necessarily has an interview either. So really just about your application in general. If it stands out there's no reason why you couldn't just get an offer straight up.