As suggested by @UKWX_ on Twitter, we're going to be looking at the Winters that followed on from Summers which contained a warm June & July but cool to average August, for analogue #11 of Winter 2018-19. August 2018 was very average or close to average on the warm side and there's little examples of Summers with such an August so I thought I'd throw in cool Augusts too but not too cool.
The 500mb height anomaly reanalysis of these Winters is a bit of a strange one. There is some blocking just to the north of Scandinavia and Russia along with Canada. There is some very weak above average heights near the Azores with low heights over top of the UK and Ireland. The blocking would usually mean increased chances of cold and snow but this looks very wet and mild, similar in vein to 2013-14. There is a large mix of Winters in there though as you should expect. 1868-69 was the mildest Winter on record and still is to this day. Meanwhile, 2010-11 had an exceptionally cold December. Winters 1870-71, 1887-88 and 1941-42 were also very cold. I think there is nothing concrete from this analogue to really come to anything, even from a month by month perspective.
The only year that comes close in matching 2018 though for the Summer in terms of actual temperatures was 1868. The fact we only have one close match says there isn't anything to be seen from this analogue.
