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The weather should be similar to the UK and there should be no need for particularly warm clothes. It can be rainy so go prepared. Watch out for the mosquitoes which can be a nuisance (they are not of the malarial type, just annoying).
We have cruised the inside passage 3 times during July/August now and have had cool,wet,warm,dry and even almost hot weather. The answer is to take layers. I find jeans and trainers are useful for tours and shorts and flip flops for kayaking, with T shirts and a fleece and don't ever leave the ship without a lightweight waterproof top ie kagoule and if you want,an umbrella.If you are booked on any tours that need 'special clothing' ie a waterproof for water based activities, it will be provided although if you intend to join an intensive hiking session it would be sensible to take your own solid footwear. I find shorts are the order of the day on board during the day with t shirts and a fleece and the kagoule if required. Glacier Bay can be cool so jeans are useful too. Do bear in mind that if you are cruising via Vancouver it could be hot.