> Someone has suggested using an old pair of sock **outside**
> your shoes (i.e.over the top of them),

If it was me, I'd be down in the shed with a bit of sheet steel and
a box of screws to make a pair of short-studded crampons

http://en.wikipedia.org/wiki/Crampons

Mind you, pretty sure the council would get huffy about the damage
they might do. My old school had an ongoing ban on stiletto heels
since the 50s because of the damage they did to the linoleum and tiles.
Still pock-marked and scratched in my days there
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