Hang on.

You forgot that the U.S. doesn't have nationalized single-payer health care, didn't you?

If the state does not interfere then you can get an abortion from a non-state-run clinic.

Only if the state interferes can you not have an abortion, because said clinic is forbidden from operating.

(You forgot that there's private healthcare on your side of the pond, too, apparently.)

In any case, I don't think you're using the word "autonomy" correctly. Self-governance generally includes the ability to enter into agreements with others. If someone else comes in and forbids the agreement, that's a loss of self-governance.

You should incorporate the medical care examples I used into your piece to make it as clear as possible that you have an...unexpected...idea of what "autonomy" entails.

Unless, of course, the entire issue is that you forgot that the U.S. doesn't have nationalized single-payer health care.