When we moved house further from friends etc my sister and I (then 15 and 13) were offered £20 a week or a phone contract and the remainder of the £80 as allowance.
Best thing my mum could have done IMO. We set up bank accounts (no overdraft obvs) and both chose the phone as well as the money. Pay as you go was too expensive then, although now it may be cheaper, so we both took out £30 per month contracts. The £50 was to cover school lunches, bus fares and socialising, as well as any clothes/shoes deemed inappropriate, unnecessary or unsuitable!
When our contracts expired we reassessed. My phone had just about died and I wanted a blackberry, so I found a £25 per month contract and get £55 a month. My sister swapped down to a cheaper "sim only" deal and I don't know how much she gets, but would guess it isn't much more than me. However, she has a serious Topshop habit to fund!. Around the same time I got a PT job, and I now have 2.
3 1/2 years ago £50 a month was a fortune but now £55 a month is a pittance. (that could be something to do with my foreign trips though)
My mum also has made me pay for half of any school trip, over £100. I paid to go to Germany in year 8 and Skiing in year 9 from money I received for my bat mitzvah. Year 10 I went to Berlin, which I earnt money for by doing chores around the house for £5 a week (nice little earner for my mum there really!) In the sixth form my dad paid my half of a Russia visit as my Channukah/17th bithday/Chanukkah present, I have raised (through working 2 jobs, car boot sales and selling knitted dolls my gran made AOT) £3645 by myself to go to Kenya for a month, and I owe my mum £450 for a trip I took to Washington in Feb 11 with school. When my student loans start I'm going to pay her back in monthly installments.
I just turned 18, and received the contents of an account my dad set up 11 years ago. With very little advice from Mum, I organised a meeting at the bank and decided how to become as independent financially as I could. I'm sure I wouldn't have felt confident enough to do this without the earlier financial awareness.
£20 is generous, but consider raising the amount you give DD - in line with increasing the amount she has to spend it on. It feels good to know that you have money to choose how to spend.