I have dual US and UK citizenship and I lost my UK Passport and need to replace it. How do I get my new UK Passport? I currently stay in the US.
The UK government has all the relevant information on its website. See: Renew or replace your adult passport. Specifically, you want the information for Overseas British passport applications. Follow the steps, choosing "replacing a lost or stolen passport," and it will tell you what you need to do, with links to the application form, guidance, and list of required supporting documents.