I just returned from a 2-week trip including Dublin, Edinburgh and London. Our travel dates were the first two weeks of July. None of the hotels had air conditioning, which we knew because it was clearly stated in the room description. What I did NOT expect was how much I would miss AC. Being from the Southeast US, we figured that daytime temps in the 70s and nights in the 50s-60s would feel cool, but the air in the hotel rooms seemed stuffy, even when we opened windows (which then invited in street noise). At home I had a small lightweight desktop fan that would have fit easily into my suitcase (I would have been willing to exchange a pair of shoes for it). How I wish I had packed it, both for comfort and also for background noise. We still had a fantastic trip but maybe this tip would be helpful to someone else.
I know the feeling. Didn't you ask at the hotels for a fan? We have had to do that.
Temperatures in July and August can easily push towards the low thirties C (90+F) in the UK and this can often be the result of a 'Spanish Plume' meaning high humidity and intense rainstorms (which was the case last Friday / Saturday). Max temp in London isn't forecast to fall below 80F until next Monday.
Having watched quite a few Wimbledon matches on TV when the temps were in the 90's, I learned long ago that I didn't want to travel to the UK in the summer months.
We were in the UK the first 2 weeks in June. Our hotels also did not have air conditioning but they did provide fans. The fans helped but it was still so very hot in the rooms. We have traveled to the UK many times, and we have had other times when the temperature has been a problem, but mostly it's been fine.