Foreign companies
This is already going on in British embassies and consulates around the world. Passport renewals and visa applications are handled by one of two companies: Worldbridge or VFS Global. Employees of these foreign companies will collect and process the application forms and photos of British citizens renewing their passports. The situation is similar for UK visa applicants, except that their fingerprints are also taken.
When my wife applied for a visa at the British consulate in Düsseldorf last year, we did not come into contact with any British staff, only local Worldbridge employees. Even the person conducting my wife's visa interview was German and complained that my wife spoke English and not German - in the British Consulate! I assume my wife's details (and my details that were on her UK visa application) are now stored in some database in the USA.