Couple of points:
First, obviously, "things should be nationalised" and "things should not be nationalised" are both ideological positions.
You say that you just want whatever works best — i.e. you're not committed to either of those positions; " I just want a good health service." Fair enough. (That's a different ideological commitment, obviously — it's a commitment to the priority of quality of service over other possible goods such as democratic control or fostering economic opportunities for healthcare providers.)
But then you go on to say "From what I have seen the State is really bad at delivering services and really bad at offering value for money". But, when it comes to the provision of health services, the data and evidence suggests, on the whole, that state-run services tend to be more efficient than privately-provided services, delivering better health outcomes at a lower cost. There's much debate as to why this is so, but that it is so is not really doubted, except by those who have a vested interest in the private provision of healthcare, or who have an ideological commitment leading to a preconception that state provision is generally less efficient.
Now, I'm not saying that you're fooling yourself when you say that you don't have an ideological commitment, one way or the other, on this matter. But your position is exactly the same as the position that you would hold if you did have an unrecognised ideological commitment, and "what I have seen" about the efficiency of state provision in this field looks to be at variance with what most people who study this topic see, so there could be a little bit of confirmation bias going on here — i.e. you notice instances of inefficiency in state provision because they confirm what you expect to find. One of the things about relying on the data and evidence is that you have to be rigorously open to all the data and evidence. This can be surprisingly hard to do.