Yes. Constitutional protections against unlawful search and seizure mean nothing if they only apply to citizens, because not everyone is a dual citizen of every country with an intelligence agency. If America can't spy on Americans, and the UK can't[0] spy on Brits, America can still ask the UK to spy on Americans that don't have dual citizenship with the UK, and the UK can ask America to spy on Brits that don't have dual citizenship with America. This makes 4A into a water sandwich.

[0] I'm assuming there's some kind of 4A-equivalent bound on government behavior in the Calvinball soup that is the UK 'constitution'