Can exercise help mental health?

In the news today I saw that some GP surgeries are being encouraged to perscribe exercise to combat mental health issues. Wishing to keep well away from the political arguments around this I was interested to see the link between the two. Anecdotally I have seen the connection - exercise as a way to help regulate the body, to help lift mood and increase a sense of well being. Research also supports this with reference to a range of scientific reasons as to why exercise aids the body. But also though I have seen exercise used as a punishment, as a way to enter oblivion, to control, which has also in its own way helped people survive but can go too far and become damaging. I also wonder about the shame or guilt associated with being told to exercise (if exercise is not part of your regular routine there may be a reason, and shaming you into doing it doesn’t feel a very healthy or positive step). A lot of my work involves noticing and connecting to all of you, our head/brain, our feelings and our physiology. And so it makes sense that as we connect more to our body we may do more with it, so maybe going for a walk and being aware of self in the world can help.