Alaska is currently offering its elite members some priority benefits on British Airways for a limited time. It's possible it will be extended and that there's some reciprocal action for British Airways elites on Alaska, but I'm only guessing.

https://www.alaskaair.com/content/de...h-airways.aspx

Otherwise, eponymous_coward is correct, the only way to gain access to the premium security queue (what the UK would call "Fast Track") is to have elite status or book a first class ticket. That's essentially buying it with Avios. Not a good price, but it's an option.

CLEAR is an alternative. It costs money to enroll and is also expensive IMO. Same security process but you move to the front of the ID check. Any US ID is eligible, including a permanent resident card or state driver license.

https://www.clearme.com/how-to-get-c...s-to-get-clear

PreCheck is a completely separate security process, cheaper than CLEAR and also better IMO. (The lines aren't as short, but that's because almost no one uses CLEAR at Sea-Tac right now.) But PreCheck has more stringent requirements. UK citizens and a few others should be able to enroll.