We saved up for our children so kept an eye on the "parental contribution" as both Dh and I went to uni and had very different financial support.
Save The Student lists out all the different household income bands so you can see what the maximum loan amount is and what your child would get if you were over the threshold for household income of around £62k.
We guessed at £5k per year so for 2 children we saved over £40k in case they wanted a 4 year course.
The reality, when DC1 went to uni we looked at what the maximum loan would be and what his minimum loan amount was that he would get. We topped him up to match the maximum amount. We then took the yearly accommodation cost from that and what was left we divided into 30 weekly payments to support him term time only as we would be paying for meals etc when he was home. That meant £100 a week or £3k which they found was plenty of money
DC2 is currently at uni and if we worked the same way they would only get £75 a week as their accommodation is more expensive from year 1. We have therefore agreed the £100 a week with them and so technically we are paying over the maximum loan amount. DC1 cost us £5k per year, DC2 is costing £6.5k.
Both my children are/were in private halls of residence for 2nd and 3rd year. A lot of universities have their accommodation costs listed out so you can see for at least first year what they would be paying. For DC2 ranges from £130 pwk or £5200 to £255 per week or £10,200. Quite a difference. Surprisingly the private halls are actually cheaper than some shared houses.
Their lifestyle and what they expect to pay out also matters. Laundry costs are listed on uni websites as are typical spends for supermarket shops. DC2 spends about £40 a week at the supermarket. Then there is Netflix, Amazon, Spotify, gym membership, course materials.
Clothes, transport, socialising etc. We wanted them to have a lovely time at uni with no money worries. Plus Freshers' Week adds another week to the first term, there are upfront fees for things like common rooms and Freshers' club nights.
Kitting them out with everything they need to take like pillow, duvet, towels etc. You might have these in, you might need to buy them. This is why we saved over and above so we had cash to spend. Also new laptops with insurance cover in case anything happened to them. We did have to drive to DC1 when their laptop died the night before an exam! Luckily we had a spare one we could take to them.
If you were my friend I would say aim to save between £6-7k per child per year but also that a lot of students work either before, during or the summers (4 months long) whilst at uni. Most students use their overdraft, you can see how much banks offer. We started saving from lower primary so had more time to accumulate money. We also saved it all in our own names because whilst the intention was to use it for them, if we needed it, it was ours to use. I know this is very long but I hope it helps.