Some thoughts:
Do you think the LL knows this girl/her family? Why did he insist she in particular move in? Is it not odd that the LL found a replacement tenant rather than the tenants? Eg If 5 of you are paying £500/month in rent and someone moves out, you’re still liable to pay £500/month. The LL generally doesn’t care who’s paying as long as they’re paid.
What are the termination terms of the contract? If they all went to the EA to say this has gone on long enough and we’re done, what are the penalties? If you’ve got J&S liability on the rent (ie you’re all liable if someone doesn’t pay) then technically she’d be liable to pay the others’ rent if they all left. They’ll know they don’t have a hope of her paying it if she’s already behind on the rent. Might make them keener to sort things out.
Point out to the LL that if he doesn’t kick her out for unreasonable behaviour then he will lose the rest of you which will cost him a lot of money. Play hardball. Yes all the parents are liable to pay the rent, but they’ll need to take you to court, it will take ages, cost them money etc, etc, etc. Get clued up so you sound like you know what you’re talking about. EAs aren’t always as familiar with the law as they should be.
Is the deposit in a deposit scheme?
Has the LL done anything else that would make them a “bad” LL?
What ethnicity is the girl? You said she called the girls “stupid white XXX” (which is racist) so I’m guessing she’s not white. Are you in contact with her dad? Would he know she’s potentially not at Uni running up debts for him to pay? Would he take that well?
Be the squeaky wheel. The EA & LL don’t really care. The property is so they’ve done their bit. It makes no odds to them if you’re daughter is living with a nightmare, being locked out and intimidated in her own home. Make it their problem. CC both of them in on the emails. Give them time limits to reply/do things. Tell them what you will be forced to do if they don’t comply. This will also give you a paper trail in case things go to court at a later sate.
If she’s not at Uni then they might not be able to help. They and the EA will probably site GDPR about not giving you information. Having a non-student in student accommodation changes the nature of the tenancy and has implications that the girls didn’t sign up to. They’ll be due council tax I believe. Will it impact his PP/HMO if he’s got a non-student living there?
Good luck!!