Just to reiterate / rephrase what people may have alluded to here, having talked about switching to the Maths and Phil course with my tutors, and having helped out at interviews and seen the process a couple of times over, I'd certainly say that your Maths ability is non-negotiable, of which an important factor is the MAT. I think for Philosophy, you have to demonstrate that you're interested in the subject and the natural overlap with Maths, and that you are able to construct reasoned arguments. Essay writing skills will be honed in the degree, so as such it's not necessary to come in with excellent written technique, though it is obviously helpful. It's not uncommon, I don't think, for interviewees who come across as very good Mathematicians, but don't quite demonstrate the pre-requisites for Philosophy, to be offered a place on the sole Maths course.
Good luck with your application! If you have any questions about the Maths side, please feel free to ask!