Any US Customs/INS/DHS/whatever office is considered "no-man's land"... sounds ominous, but it really just means you're standing on US soil, even though you got off a plane in Canada. Above posts have hinted at the answer here... you do all of your US entry and exit "stuff" at the cruise terminal in Vancouver. It's a big, and relatively new facility, and usually goes quite quickly and smoothly. You'll carry your UK passport with the US (and presumably Canadian) immigration marks, visas, etc. with you while you're cruising. If you need ID for anything in US ports, just use your passport.
When you disembark in Vancouver, you'll go through a similar (reverse) process to officially "leave" the US and re-enter Canada, at which point I run out of answers... presumably you'll re-enter the UK when you leave Canada and return home, but I've never undergone that particular phase.
(My horror story is getting through Ukraine on my way back to the US from Russia... Russia was fine letting me in and out, US was fine letting me out and back home again, but Ukraine had big problems with my laminated reproduction of a US confederate bill from the Civil War as a bookmark in my Tolstoy!)
Better not for now... signatures get me banned!