I think that £170 would easily be enough for everything except transport, as long as she spends it a bit more wisely. £150 is do-able, but only if she already has dress shoes or good make-up supplies.
For example - dress agencies will charge less than £100 for a lovely, practically new and high-end highstreet/low-end designer dress, and there are lots of bargains to be had on e-bay too if she's prepared to look carefully. Alternatively, there's an online company called Light In The Box which sells gorgeous dresses for fantastic prices - just need to factor in customs, shipping time and delivery costs from the US. I'd budget £80 for that.
With make-up - if she wears make-up more than a couple of times a year, it would be more cost effective to go to some counters and get the assistants to show her how to choose and apply it so she's happy to do it herself. MAC offers a special deal where you pay £20 for a "makeup lesson" in which they show you exactly how to create the look you want, and you can then put the £20 booking fee towards products. I wouldn't recommend their foundation (a NO7 counter will help her to find a good colour match for under £15), but she could get her foundation applied at a different counter and then get the MAC bods to show her how to find the right shades of blush, eyeshadow, lipstick etc and apply them well. If she's doing her own make-up, she will definitely need a foundation brush at the very least - Real Techniques (from Boots) give the best finish for "drug store" prices IME and are very easy for novices to use, she couldn't possibly go wrong with the Expert Face Brush, and any old powder and blush brushes will do. IF she will wear it again, I'd budget £50 for make-up supplies (assuming that she doesn't already have the things I've mentioned).
Shoes are the real bugger, in my experience - New Look is generally the best for cheap-ish, fairly comfortable formal shoes and usually come in at under £30. I'd budget £30 for shoes, unless she already has some that could work.
The extra tenner would be for hair supplies.
NB - My prom was about 8 years ago, and my dress was £40 from TK Maxx, my shoes were £10 from New Look, my make-up was shite because nobody taught me to do it properly, I went in the family car, and my hair looked dreadful, courtesy of my mum. My folks would happily have spent more, but I just wasn't bothered - I only went because my mum made me. In retrospect, the only thing I regret was the make-up - it would have been a good opportunity to get some nice stuff and learn to apply it properly for the future. Despite all of that, I do think that what you "should" budget for this comes down to what is reasonable for your family's finances, what your DD is prepared to contribute (either in the form of money or labour), and what it will take for her to enjoy the evening without feeling self-conscious - not what any of us tell you.