I'm a University student in the UK too, welcome to the forum!
I live in the UK, and there you can live off campus if you want to. I was planning on living in a dorm for at least the first year, but I've heard of people bringing in small pets like guinea pigs before without a problem.
If you bring a GP into a Halls of Residence or University owned property, YOU
WILL BE FORCED TO REHOME THE ANIMAL OR LEAVE THE PROPERTY. I can't stress this enough- I've seen so many of my friends give up small animals in their first year because of misguided beliefs and carelessness (sometimes to shelters, not their family homes, too). It's standard for literally every single Halls of Residence I've encountered. The only exclusion they make is for service animals, and even that's unlikely. If you have a misguided belief you can "hide" your guinea pig, you can't. Cleaners visit the property on a daily or weekly basis and a guinea pig's cage is large, far too large to hide. It isn't a hamster, after all- you can't just pop it into a hideaway cupboard for an hour or so when the cleaners or inspectors come a-knocking. Your only hope would be private student accomodation, and you would have to BEG the landlord. I had a two-month long argument with my landlord to be able to keep my guinea pigs at the flat, and I know that University accommodation would not have given me that option, point-blankly.
I think you should certainly wait one year before you make any options to get another guinea pig. The logic behind this is simple:
In your first year at University, you are almost always encouraged to have University accommodation, which will not allow you to keep guinea pigs; you'll essentially be purchasing another guinea pig for your mother to care for, and that's not responsible, even if a friend is better for a guinea pig.
First year in University is HECTIC. Your social life is up in the air; you're getting used to new methods of teaching and higher workloads, etc.
If you're absolutely, one hundred percent sure you want another guinea pig, I would still advise you take the mature method and wait until your first year is completed before making any decisions; chances are in the first year you won't be able to bring your original guinea pig with you anyway. After one year in university you will be able to tell if you can handle the extra responsibility or if it's simply not practical- ESPECIALLY financially, because funding is scarce and living costs drain what little support we get.
Hope this helps, and sorry if it's not what you want to hear!