Stamford Hill is a largely hassidic community in London, so it is not surprising they don't want the women to drive. They simply are not making Purim an exception despite knowing that many of the men will be consuming too much alcohol and will be unable to drive.
What about tzniyus says a woman cannot drive?
The two reasons I have heard are:
1. Being the driver means having to wear an across the chest seatbelt, and such a strap accentuates the woman's breasts, making it not tzanua. I am not sure why I have never heard that women should not sit in the passengers seat, as that also has such a seatbelt. In modern cars seatbelts in the back seats are no longer across the lap but also across the chest, so maybe women should not even get rides in cars.
2. Women should not be outside in a position of power as a driver. This is some sort of application of Kol Kvoda bas melech pnima. A further explanation of this is that it gives women inappropriate freedom in mobility.
The joke is obviously that women never drove back in the days of Moshe Rabbeinu or even in the days of Chazal, so they can't start driving nowadays..
If you are aware of other tzniyus reasons for a woman not to drive, post them in the comments.
Anyways, with women unavailable to be designated drivers for their drunk husbands, you might want to be extra cautious on the streets of Stamford Hill this Purim...
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