Is there any school out there that actually tackles bullying and peer-on-peer abuse properly without gaslighting the victims with insulting, meaningless buzzwords and flat-out denying that it exists? First, the nasty child bullies the victim; then the school doubles down and bullies them again.
I'd email the headteacher (so you have a 'paper' trail) and ask him/her: "If a member of your teaching or other staff punched you in the face from behind, grabbed you around the neck and tore your clothes, knocked you to the ground, or pinned you up against a wall and put their hands put around your neck, how would you deal with this 'friendship issue'?"
Unless they come back to you contrite, furious on your behalf and determined to act, take it to as many people as you can think of and tell them what the school's clear response is to violence. Send the head a second email to tell them what you're going to do. LEA, OFSTED, your MP, police. Local papers and SM groups can also help, as bad publicity spreads like wildfire. Once the Anytown Gazette gets hold of the story of Littleton School's problems with violent bullying that they can't/won't address, it will stay on their website forever and come up every time a potential new parent Googles the school name with 'bullying'.
Also, if you feel the need to do so, inform them in writing that you will be keeping your DD off school until they can demonstrate that they have now made changes to guarantee her safety whilst under their care. They will get frantic about the impact on their attendance records and talk about fining you etc.
Again, tell them that you realise the importance of attendance and that you very much don't want your DD to be robbed of her right to education, but her safety and wellbeing are the top priority and, again, you are very willing to discuss the whole situation, the dangerous school setting and the changes that need to be made in order to provide her with a safe place to learn with any authorities that wish to meet with you about it.
You absolutely shouldn't have to do this yourself, as they have shamelessly betrayed you and summarily failed in their duty to you and to your DD; but if they see that they can either deal with you OR deal with you plus people and bodies that have authority over them and widespread publicity, they might just spring into action. Sadly, you have to make it their problem, with negative consequences for them - as they couldn't care less when it's only a problem for you and your DD.
ETA: x-posted with FofB (I got distracted whilst typing)