when i won a few years ago it was about 5,000. i asked the sun times travel editor.
as i post answers to it every week on uk.rec.competitions
(this week YORK, NIGHT MAIL) i would expect 10,000+ entries.
I submitted through the web site and won a week in Italy (and very nice it was too!)... If I am not mistaken they receive about 6,000 entries a week...