Oh it's achievable, we just need that bit of "luck" so that the cold falls inside one calendar month. As has been pointed out, the month from mid-December to mid-January has averaged very close to freezing - since the Victorian era, only the legendary 1962/63 and legendary (first half at least) 1981/82 have had colder month-long periods so early in the season. However, since the cold has spread itself fairly evenly across two calendar months, the actual monthly CETs haven't been that impressive. Conversely, the likes of January 1985 and January 1987 have seen cold periods fit neatly into the calendar month. February 1986 saw the vast majority of that winter's very cold spell, hence the extremely low CET (-1.1C). The coldest month ever recorded (January 1795) saw the cold fit almost perfectly into it (only 31st December - 30th January was slightly colder than the calendar month).
The same applies to heatwaves and summer months - like its cold counterpart January 1795, the hottest month ever recorded (July 2006) was only a day off being "perfect" (with the period 30th June - 30th July being only slightly hotter).
The timing of the prolonged cold this winter hasn't been kind to monthly CET-lovers (myself included ), but it has still been rather exceptional.