As much as I don't understand the whole 70k household but unable to support daughter, let's just try and be productive here and go with it.
student finance gets you tuition fee loan and the maintenance loan of £2871. (correct me on those numbers of necessary)
I don't know where the £100 for food estimate came from, middle class uni students eat at £50, if not £30 a week. She shops at tesco from now on, and until she works out financing properly, she does not drink or otherwise waste her money. If she's not capable of this self control; then she's not ready to be independent.
Depending on where your daughter is going affects the living costs and accomodation.
London based unis have high accomodation costs. A friend of mine who is attending RADA (however you spell it) is actually staying at a girls only youth hostel. I'm just going to assume its less than regular out of london accommodation. Because there is no way in hell you're going to pay the 6k regular accomodation of london unis. If she argues then she takes out one big loan or she doesn't go to london, its simply not do-able otherwise.
outside accomodation maximin is around 4.5k. (Yes a maximin, that's not a typo)
so you need 1.8k + living costs (hypothetical numbers), just to get started (going by each year)
However the only initial costs for university is the first in bulk payment for accommodation (the first side of the 3 month contract) going with the 4.5k - we'll call it 1.5k; as well as all the school books and equipment, gym pass, bus pass and so forth and finally as a safe provision, 3 months worth of food money. that comes to about 2k, give or take £100.
your first initial 3 month installment of your maintenance loan comes to £900 ish.
so she need 1.1k every 3 months extra to be safe and comfy.
So you can give her 1.1k near enough and tell her to get a job during the first 3 months of uni (get to the accommodation the earliest possible and get job hunting / look up the market now and apply)
or she can get that 1.1k start up cost by working through the summer holiday / out of her own savings.
now for the next three months after that, again I'm just going to carry the 1.1k - because its late, I'm tired and the information is very vague (seriously PM me all the exact costs, which university and preferences for jobs and any further questions and I'll plan it all out)
so 1.1k every 3 months
rounding it up for comfort - £400 a month (dat rounding tho)
that's £100 a week.
minimum wage is 6.50 ish. She works 16 hours a week as a part time job and she's perfectly fine for every 3 months thereafter.
option 1: front her £1100 - I dunno how viable it is. She'll get a job within the first three months and job's a goodun.
option 2: she raises £1100 by herself from summer holiday jobs and then send her packing and she get's a job within the first three months and job's a goodun.
option 3: persuade her to take a gap year, if she works just 20 hours a week at minimum wage for 40 weeks. that's 5k. she'd have a much easier time of all this, plus her CV would shine even more and she'd find it easier to get employment at whatever place she's going to uni. (this will be the best option if she's absolutely dead set on a London university and won't stay in a hostel.
if you say funding 6k is out the question each year (and quite frankly even if I had the money I wouldn't fund them every year) she's getting a job during university. If she rejects this idea, she's not ready to go to university
This is probably the haziest set of figures I've ever had a look through but they're a rough idea. I'm effectively assuming she'll live on 6k a year here (which looking back through is what you listed it as, which is somewhat reassuring)
Again PM me with more exact details and I'll try and make this as accurate as possible.
I Hope this helps - seriously, this took half an hour at 1AM.