I can very easily imagine myself being in your position. I have studied at York (Masters) and appreciate the attractions of both the university and the city. I am involved in education research and I too was interested in Political Science as an undergraduate.
If you want to hold out the option of secondary school teaching as a career, it might be advisable to include a teaching subject in your degree programme; for example History and Politics, which York offers. You can then pick modules that make the degree more Politics oriented, but still be qualified to teach History.
You could take the same route for primary teaching, although a professionally orientated Primary Education degree, with integrated teacher training, would be ideal for someone who was certain that they wanted to work with younger children.
The Education Studies BA at York is an academic degree and so does not lead to a teaching qualification. There are several option modules that do relate to the politics and sociology of education but you would be no closer to qualifying as a teacher than with a Politics oriented degree, with or without a teaching subject.
In short, if your priority is to go to York, and you think you can get the grades (AAB), I'd opt for Politics, preferably combined with a teaching subject followed by a PGCE specialising in whatever age range you were interested in teaching. If in time you decide that teaching is not for you, you'll have a degree with a broader academic currency. You could always choose an Education degree as an insurance option.