Weather on individual days has been notable yes.
But in the final analysis it will end up a wholly unremarkable month as the extremes all end up cancelling each other out
Plus despite all the media hype , there haven't really been any proper extremes. No individual day or night has produced jaw dropping mild or cold temps (the very low temps of the last 2 nights have been the coldest in Jan in SE England for some years and much hyped in the media yes, but that speaks to a lack of recent cold Jans more than anything ), it's just a marked step change from a mild wet first half to a cold and dry second.
Will be interesting to see what Feb brings now as it very much holds the balance of power now with respect to how the overall winter will be remembered .