I've put the CET data series into a spreadsheet and done some
processing. I reckon that the mildest runs of winters are as follows.

5 years: mean of 5.4C - 1972-6
6 years: mean of 5.2C - 1971-6 and 1734-9
7 years: mean of 5.2C - 1733-9
8 years: mean of 5.1C - 1988-95 and 1732-9
9 years: mean of 4.9C - 1992-2000, 1988-96, 1987-95, 1920-8, 1919-27,
1918-26
10 years: mean of 4.9C - 1989-98
11 years: mean of 4.9C - 1989-99 and 1988-98
12 years: mean of 5.0C - 1989-2000 and 1988-99

Bear in mind that the differences between those sets shown and the next
mildest are often only 0.1 of a degree, so are very small, and so
rounding could become a factor (I've rounded all the values to the
nearest 0.1 of a degree). The December values are credited to the
following year (eg Dec 1976 counts as part of "Winter 1977"). The mean
value for the run of 12 years may seem anomalous. It is at least partly
an artifact of rounding.

Those who like cold winters may be able to take some heart from what
followed the mild winters of the 1730s. And there is at least a
slight hint in the data that the mildness of our winters may have
declined a little post 2000.

The runs of coldest winters are all back in the 1670s and 1680s.
--
John Hall
"Acting is merely the art of keeping a large group of people
from coughing."
Sir Ralph Richardson (1902-83)