This year it runs from 31st December 2022 to 3rd January 2023.
New Year Plant Hunt 2023 – Botanical Society of Britain & Ireland (bsbi.org)
At 3 hours per list in principle you can produce 12 lists over the period, weather permitting. You can generate morning and afternoon lists easily enough. To manage a 3rd daily list you either have to shorten the observing period on one or more lists, or do an urban evening list by streetlight. (The weather was favourable last winter, and I managed 10 lists.)
The long term forecast is for the current cold spell to have broken before the turn of the year, but the cold spell is likely to see off a lot of late flowering plants, so I’d expect fewer plants in flower than last winter.