[Solved] Ex trying to stop me from seeing my child

Here's the history for you: I have a 4 year old with my ex - we split up when my son was just 4 months old and I have always been in his life. Before he started pre-school i had him at my home two days per week (i worked from home) and after he started pre-school I picked him up one afternoon per week and had him at my house for around 5 hours. Basically I have spent quality time with him every week he has been alive.
The current situation: I moved house, I am now about an hour from my son. Since moving I have tried repeatedly to see him (his mother has taken him out of school) but everytime I ask about his availability to see me, she says he is busy. This has gone on for 12 weeks. I haven't seen him since just after his 4th birthday. for the last 12 weeks she has been pushing me to agree to a regular day and time months in advance but my new job has odd hours and I don't want to commit to plans that may have to be broken at short notice. I have Parental Responsibility for my child and I have asked her to allow us to have contact on a regular basis again. I have asked her for his weekly availability so that i can try to find regular times to see him but now she has emailed the following:

"I take care of all of XXXX needs, from education to health, entertainment to nutrition. That is parental responsibility, not video chats, £70 a month and afternoons out stuffed with sweets and toys. As a parent, my life fits around XXXX, not the other way around. It really is unfair that because there is a biological connection you feel the need to disrupt his happiness and well-being by continuing to press for visits when you can't offer regular times, because of your work. It seems you working patterns lend themselves to being unreliable with respect to child care arrangements, would the mediation service look favourably upon this when my setup is solid as a rock?
It is a shame this issue is about you and your need to be in XXXX life, because what you are offering him isn't exactly a healthy relationship but as long as you get what you want, who cares about an impressionable 4 year old boy and his reactions to your situation?
Hopefully, in time, you will consider all of my points and relinquish all parental responsibility to me, the one who provides a complete and healthy life for XXXX."

I now understand that she just wants me out of his life and that whatever I try to do she is going to block me at every turn - as she has been ding for the last 12 weeks. What are my options here???

She is saying the only time he will be available is between 4-8 on weekdays but this is when i work and she knew this. Can she really stop me from having contact with my child like this???

There is more than just a biological connection between us, he is my child and we have an emotional bond that she can never break. I have never filled him full of sweets and toys, my time with my child is spent at home or in the park, we always sat down to a good balanced meal and I bathed him before taking him home to her.