Are you watching The Crown with German or English subtitles?
That's actually the key issue - British English sounds faster and "blurry" because the pronunciation is less distinct than American English. Americans articulate more clearly, that's true. But it has nothing to do with you having learned too much American English. Your ear just isn't trained yet on these intonation patterns. The accent itself isn't faster, but the vowels are shaped differently and consonants are pronounced more softly - it feels like mush when you're not used to it.
Here's a practical tip that a lot of people forget: watch scenes without subtitles, but not to understand them, just to listen. Really just 5-10 minutes at a time, several times a week. Don't try to catch everything - just let the language wash over you. Along with that, it helps to watch British YouTubers or podcasters where normal people are speaking (not actors doing that overly artificial RP). After two or three weeks you'll notice your brain starting to pick up on the patterns, and suddenly The Crown flows a lot more smoothly.