I am from Seattle Washington in the United States which is about 150 miles south of Vancouver. I will be driving up for LTX and I have been to Vancouver Multiple times because it is such a great city and relatively close to home. In late July it will be hot (85-90F) and it won't rain that much if at all while you are in Vancouver. I would definitely only pack one or two sweatshirts and I highly doubt you will need them. It's usually not humid so it won't be sticky but it definitely will be hot. If you have any more questions about Vancouver feel free to respond and I will do my best to answer them. Enjoy your travel to our little part of the world and I hope to visit the UK one day!
Thanks,
Patrick