I did this trip in June many moons ago, and I expect the temps to be similar in aug sept. I used a lightish summer bag and dont really have recollections of ever being cold, always had a fleece with me and a pair of long pants for the evenings and mornings.
Take a peek at various places along the route for expected temps in those months and you should be able to get an idea of waht to expect.
Being from Blighty, you'll be at home (not for rain mind you) that june trip was the coldest june I had ever experienced, here in the east of canada, its not uncommon to have 30c days in early june sometimes, and it seemed to me taht the west coast trip was rarely above 20, maybe 25 tops, but usually a bit cooler. Nice riding weather in other words.

are you completely new to camping?

enjoy the trip, its a neat part of the world to bike in. It is hilly in some areas, so do make sure you have reasonably low gearing.
Again, enjoy it. Oh, use a mirror, it can be busy sometimes and having a heads up behind is always a plus when bike touring.
cheers