TBH given the state of cities today if it were my 18 year old daughter despite my environmental concerns, if she has a driving license I'd actually try and find the money for her to afford a car, particularly if she ends up having digs in a less than pleasant area of London, and/or her job involves lone travel in more outlying areas especially after the hours of darkness...
my younger sister remained in Reading and she drives everywhere for work, leisure etc - she is otherwise quite eco-concious - and this is for reasons of personal safety and independence!
Although Reading isn't quite as bad as London there have been some very nasty incidents against lone women in recent years, and my sisters friends have been harrassed and stalked etc by strangers so I don't blame her one bit for driving, I'd rather she had her independence and I blame the misogynistic scum what infest this nation for the potential environmental damage, rather than young women for "choosing" to drive. Only this summer the Grauniad ran a long article on the amount of harrasment female cyclists were experiencing in the capital and of course metpol is so overloaded with dealing with genuine real crime (shootings/stabbings/rapes) they hardly have any time to deal with these crimes.
I've also been told by several young ladies/women who both drive and cycle who say they enjoy cycling but feel doubly unsafe on two wheels, as much from gender related harrasment as from the usual road safety issues, including incidents where a girl has tried to stop idiots in a car from groping her / pinching her behind and has been shoved off her bike into the gutter as a reprisal whilst the scum drive off...
A lot of "right on" ladies on places like debates with George Monbiot have also pointed out this "elephant in the room" a fair few times in debates over why cycling tends to be a more male dominated pursuit..
OK I expect cycling or using public transport in broad daylight and well watched or "better" areas is probably perfectly safe in London but it still ends up with people having to modify their behaviour (handing a victory to the scum) and I won't begrudge a young lady using four wheels if she feels safer (that is provided of course she drives safely too which I'm sure eddios daughter does, same as my sister..)
maybe there are car share clubs in the region she is staying? perhaps she could get a cheaper bike for "safer" times and use the car share otherwise?