Looks like the final answer is (finally) in: 6.39c, found here: https://www.metoffice.gov.uk/hadobs/hadcet/cet_mean_2020
I quite like that representation of the data and I've discovered that if you change the year in the above URL, you then get the data for that particular year so you can actually find out what the CET value was for any given day within any given year, just from this data alone.
I've also discovered that the top line of this data appears to be the temperature anomaly for each month as set against the 1961-90 LTA, rounded off to the nearest 0.01°C and then multiplied by 100. The actual user-friendly pages on the Hadley site which Gavin P. shows in his videos, then shows those anomalies rounded off to the nearest 0.1°C.
From that, we can see that last month's CET figure of 6.39°C was 2.58°C above the 1961-90 average if I am correct in what I have said in the last paragraph. In the final Hadley page which Gavin P. will no doubt evetually show us at the time, this will then be likely to show up a value of 6.4°C for January with a temperature anomaly of 2.6°C above average.
Gavin P. (at least whoever it is that helps him to maintain his website) has brought together an excellent list of all of the CET data on his site which goes all the way back to 1659 and after studying that, I have discovered that last month was the joint 14th warmest January on the CET records going all the way back to 1659, and the 4th warmest January of this century according to those same records. As Gavin P. has said on his videos, we have to go back to 2008 to find a January which was as warm or warmer than that, and this is shown up really well on the data on his site which I have just mentioned.