I think you'd be better off posting in Higher Education. Costs will depend a bit on whether the university is in Kensington or New Cross and what they are studying, whether they need material/equipment, books or have field trips.
£160-£170pw for 52 weeks is about average for a room in a shared house with no living room. University halls are more but there are no bills and it is term time only (usually only for 1st years). Private halls are £250pw upwards (and the sky is the limit).
Utilities/broadband/TV license/insurance are probably about £30 a month. There are no bills in halls but laundry is £2.50 plus drying.
Mobile could be anything from £5 to £100 depending on whether it's a sim card or they are upgrading to the latest phone every year.
A weekly travelcard is around £30. They may not need one if they are on campus or live nearby. The daily cap on the Oyster card is £7.40 so budget that for every day they travel (not just for uni). Mine usually get an Uber with friends if they go out late, it is often cheaper (per person) than the tube.
Groceries - £30 per week is average but going for a coffee or lunch on campus is high street prices and that wouldn't cover many of those. My DC's university's suggested budget says their students spend £60pw on average!
Books/equipment/field trips really depend on the course and the uni. Mine had pretty much everything provided and there is funding for field trips for students who can't afford them. They spent about £250 a year on average but most of that was on field trips/conferences.
Entertainment - going to the student bar once or twice a week is average, there a usually a couple of big events a year (balls, formal dinners, uni club nights), the odd big night out, birthday dinners, club subs are cheap (£20) but there might be a sports or music tour, possibly abroad, uni gym prices vary. Freshers' Week is expensive...
Then there are clothes.
The uni budget suggests the average is £46pw on entertainment and personal spending.
As well as the loan of £12k, their uni has generous means tested bursaries of up to £5k, so I guess £17k per annum is a fair estimate of what they consider it costs for a decent standard of living, being able to afford to take opportunities like field trips etc without needing to work during term time.
It's possible on a lot less but that isn't what you asked.