A few days ago me and my partner had a massive disagreement on the welfare of my son,
This was the first of many.
After this disagreement I told her we needed some kind of mediation and with that she told me that I was'nt allowed to see him.
Now she has told me that she has already been to see one,
Could you please tell me on what grounds she has to do this?

Grounds ?

To establish a written legal custody of the child, with set rules as to visits, and other issues.

You should have long ago done it,

Argement with her will do nothing, and if done in front of the child is extremely wrong

Get an attorney and make the custody/visitation a court order.
No arguing with one of those.

I am doubtful that a mediator would "mediate" with one party and half the story.

But having an attorney , (this comes from experience) is the only way to approach this.

Sooner is much better than later.