You seem to have a good understanding of your subject area and concentrations. This is a good sign and you know that fit and cost are key metrics. A friend applied to MA Political Theory and had some of your programmes on his list. He looked at research clusters (areas of excellence) and articles in peer reviewed journals from his profs. He said that for some core textbooks, unis use the similar reading lists with variation in academic articles. I think LSE prides itself with the largest Political Theory group in the UK. Normally most lecturers are from politics, philosophy and law department. Incidentally Warwick, UCL, Ox and LSE have strong track record in REF. I think Oxford's 2 year MPhil is competitive with higher cost of living. But if you can get a high 2.1, great references and strong personal statement will make a good application. My philosophy: Better try and fail than asking yourself what if. Worst case: you can only lose the application fee. If you have specific queries, I am sure the programme coordinator can help. Some reply to email queries, others don't.
With regards to financing, I would suggest to use a Excel spreadsheet and insert numbers for all unis (tuition, living) to get a comparison. I am sure you can get templates on the internet. Check for slim funding/scholarships. I ended having a ranking for fit and affordability. Count your lucky stars as you have housing sorted in London as it is a big expense item.
Unfortunately I am not familiar with York's LLM and cannot comment on it. I know that York is well respected in some politics areas such as governance and Public Administration. The course is managed by the law department rather politics department.
Good luck.