The trouble with this kind of claim is that "the range of historical statistical data" does not provide clear boundaries.
A number of record high temperatures have been set this year. By definition a record is outside of "the range of historical statistical data".
“The first six months of the year have made it the hottest La Niña year to date on record,” said Clare Nullis of the WMO.
Taiwan is the most recent place to report a new high with a temperature of 40.3C in Tianxiang on Monday. This followed a flurry of other anomalies.
Last week, a weather station at Ouargla in Algeria’s Sahara Desert, reported a maximum temperature of 51.3C on 5 July, the highest temperature reliably recorded in Africa.
In Europe specifically this year has not quite set a record overall, but individual records have been set:
In Europe, the WMO has warned of droughts, wildfires and harvest losses after the second hottest June on record. Over the past two weeks, records have been set in Tbilisi (40.5C), Shannon (32C), and Belfast (29.5C)
A better way of thinking about exceptional weather events and climate change is to imagine rolling a loaded dice that comes up six half the time. If you roll it once and it comes up six, is that because it was loaded, or would it have rolled a six that time even if it wasn't loaded? The most you can say for that one event is that the six was probably due to the loading. Now suppose you roll it 100 times and get 47 sixes. That might happen by chance even with an unloaded dice, but it is so fantastically improbable that you can say the result is "no question" due to the loading and ignore the tiny probability that an unloaded dice would have done the same.
In the case of 2018 weather, I would interpret Prof. Allen's statement in the same light. In his expert opinion the extreme weather events around the world at present would be so unlikely without global warming that the possibility can be discounted. If global warming is affecting weather globally, then of course it is also having an effect in Europe because Europe is part of the globe.
So yes, there is scientific support for the proposition that global warming is largely responsible for the exceptionally high temperatures seen around the northern hemisphere this summer, including in Europe.