You should check with both the US and Canadian Embassies in Reykjavik first. You will definitely be going through US Customs & Immigration in Seattle prior to transferring to the Canada bound flight. As Seattle has no Canada Border Services Agency Customs pre-Clearance facilities, and there are no 'sterile' International Passenger Lounges at SEA-TAC Airport, your arrival into Seattle means you are entering the USA, and may require a entry Visa.
Under the terms of the latest border control legislation initiated by the US Congress, the TWOV (Visa Waiver) program has been virtually eliminated. You will probably need a valid Passport and an US entry visa just to enter the USA (even if transiting through).
You may wish to fly directly to Canada (Toronto) via IcelandAir, and use Air Canada or WestJet (or even Via Rail Canada) to get to Vancouver. This way, you avoid having to go through US Customs & Immigration.
You should also enquire as to whether you need a entry or residence Visa for Canada (at the Canadian Embassy, of course). A work visa for Great Britain may not 'cut the mustard', so to speak, in allowing you to enter Canada.
All of these things I've mentioned depend on the nationality of the passport that you're travelling under.
A Canadian Travel Consultant.