On checked bags you are within the limits by miles. You're allowed up to three items each, and each item can be up to 32kg. Contrast with the *A limit of 30kg in business and 40kg in First (although my experience is that *A bend the rules, whereas BA's very generous allowance is absolute).

The rules about the laptop bag are a bit unclear. They used to simply say one piece of hand luggage of the specified dimensions plus one laptop bag, handbag or briefcase (nothing about a camera bag being allowed). They didn't specify the dimensions for this second item, which obvously led to potential abuse. Now they have specified the dimensions, but it's not clear if something within the dimensions but which clearly isn't a laptop bag, handbag or briefcase would be allowed.

I think you'll be ok. But couldn't you repack so your camera is in your main item of hand luggage and some other stuff is in a laptop-style bag? Note the laptop bag doesn't actually have to have a laptop in it.