I (BE speaker) hadn't heard of the "up" version until I saw this and checked my Oxford Dictionary of English after seeing nizha's comment. Whether a BE speaker uses "up" or not probably depends on his/her age. Although the online Chambers has only the "up" version:http://www.chambersharrap.co.uk/chambers/feat...
my Chambers Twentieth Century Dictionary (1972) has only dressed to the nines
Incidentally, try as I might, I just can't get the same google statistics as odondon, so I don't know what's going on there...
"dressed up to the nines" site:.uk gets 1060 hits
"dressed to the nines" site:.uk gets 523 hits
So about 2:1 in favour of the "up" version (though might the average age of people using the Internet be a factor there?). All the more reason to leave Google out of this, I'd say.
I wouldn't say the "up" version was preferred
in BE, but the ODE (which favours the "descriptive" rather than the "prescriptive" approach) suggests it is at least prevalent nowadays.
I also agree with hm--us about using "dressed
..." rather than "to dress ..."