Is Politics/PPE/Politics with Parliamentary MA Competitive?

Cannot talk out of personal experience, but I'll try to give you some thoughts.

Honestly, I would not expect a PPE MA to be too popular (hence particularly competitive at the application stage). PPE is very popular for undergrads, but I wouldn't assume the same at grad level. Not sure on this, but yet... Also, given the interdisciplinary nature of PPE, I would expect a higher degree of variety in applicants' backgrounds for that MA, than for the others you listed, and this might help you a little bit. Sheffield is a top department, so I would expect it to be the most competitive among your choices. Finally, Leeds surely attracts people for the parliamentary concentration, but it is a little more specific (in the title at least), so my guess is that only people with that very specific interest would apply (but this might not play in your favor, unless you have some relevant studies/experiences/research in the field). In terms of popularity I would say Sheffield>Leeds(slightly)>York>Kent. However, this is always a guess, so the situation might be very different. Much also depends on your PS, given that you are changing field.