I use wunderground.com to see actual day-by-day temperatures going back more years than I try to check. I don't dress for averages. I dress for how cold it might be when I head out of the hotel in the morning on each particular day, and how cold it might be when I'm out at night. I've linked to London's weather for July 2017. You should be able to find stats for somewhere near the Outer Hebrides if not actually on them. Choose "History" then "Monthly", adjust the month/year, and scroll down when the screen re-paints. Definitely check multiple years, especially for the northern locations, to get a clearer idea about the range of what you may experience.
During a long visit to northern France, southern England and Wales last summer, I learned that it was prudent to carry my (hooded) rain jacket with me every day, because the sky usually ended up looking threatening at some point. I seldom actually got rained on, which went a long way toward keeping me comfortably warm.
I packed a pair of lightweight polypropylene long johns and wore them most days. I figured why not? I walked a lot but wasn't doing heavy hiking. My outer warm layer was a relatively light fleece jacket, then I had the waterproof jacket, which also served as a windbreaker. In retrospect, I should have paid more for a vented jacket with Goretex or an equivalent product, because I was sometimes sweaty when I had the jacket zipped up.