Sadly I have a lot of experience of this, even moving schools didn't resolve it.
Firstly, you need to enter into the formal complaints procedure with school. Make sure you follow the complaint up with a meeting, and take a list of questions in with you along with a pen and paper to take notes.
Schools will always say it's difficult to permanently remove a child, and it is. But assault should be an instant removal, there's no ifs or buts. So you need to check their policy and query why they are not following it up.
Once school have responded to your complaint, you can go to OFSTED. Email the complaint, and copy in the head of governors so they are aware.
Finally, you need to email school and explain that you are keeping your child off school due to safeguarding reasons. Ask them what measures are in place to protect your child, and how you can be assured that they will be safe. The important bit then is to send your email to your school welfare officer at the local council, explaining why your child is off, and noting that you have asked school to take action. This will avoid you being fined. The LA will also follow this up as they will want to know why your child cannot safely be in school.
AND, don't back down. I kept returning my daughter, she would have her phone and the SECOND the safeguarding failed she would ring me and I would go collect her. This went on for months and isn't for the lighthearted. Thankfully I had a very understanding boss who would just let me leave my desk to go get her, but it's hard work. I became THAT parent at reception. I became the parent who sent 100+ emails. And I'm THAT parent who got those bullies removed.
As a result of all this, my daughter has missed a lot of school. So I have to take ownership of the fact that she might not get the best results out of school. But for her mental health, and knowing I was behind her every step of the way, it was totally worth the effort. Now the bullies are gone, she is in every lesson. She attends every revision class. She has a small, but ok group of friends. And she's happy.