We usually suggest that new students don’t visit home for a couple of weeks because this is the time when friendships form and experience shows that students who miss out on the first few weeks are quite often the ones who struggle more throughout the year
This advice is excellent, and what we say also. We found that if even the most homesick students could stay until Reading Week (usually Week 6 or 7 of the term) and then go home, they realised how much they were enjoying their independence, and how tricky it could be to be the "child" again!
I'm a Northerner teaching in a northern university. About a decade ago, we put a lot of pressure on the Student Union not to have an alcohol-focused Freshers' week, because our Muslim & Hindu students were excluded. So she won't be the only one not drinking.
She really needs to be a bit more pro-active: join societies, go out of her way to talk to people. Maybe you could help by rehearsing with her some open conversation starters (and NOT "Where did you go to school?" or "What were your A Level results?"
But do a bit of tough love & encourage her to stay at university on the weekend - maybe you could go to visit her, and you could do some exploring of the city where she is. Do a free Red Coats tour, for example?
I'd also say that at my university, it's the soft southerners who are looked down upon - in a gently teasing way! We have to teach them our ways of dealing with drizzle & short days.
But I suspect this is in your DD's head, and not overt cruelty from her flatmates.
Homesickness is real, but it passes. It's nothing more than slight fear of change. Encourage her to enjoy her independence!