British Accent help

You are hearing it correctly. That is not the usual way to say it. I've never heard that before, but it makes good sense. It sounds like a good, novel sentence in English similar to "How about I drop you off?"

Thanks, Englishmaven.

Do you find natural the construction "Why not I drop..." intended to mean "Why don't I drop..."?

Strangely, all the scripts found in Google say "Why don't I drop..." for this trailer.

I'm a native English speaker in the US, and I hear: "Why don't I drop you off on the second?" But this is said with a pronounced British accent, so it comes out sounding something like: "Whynon't I drop you off on the second?"

Thanks, Anon.
Is this type of British accent commonplace?
I hope maybe somebody who speaks British English could confirm all this. I'd appreciate it.

This speaker of BrE heard 'Why don't I drop you off on the second?.The accent is moderately similar to my own, and so it sounds natural to me.

fivejedjonThis speaker of BrE heard 'Why don't I drop you off on the second?.The accent is moderately similar to my own, and so it sounds natural to me.

Thank you very much.

listeneverIf so does it make sense?

Yes, it makes sense. He's referring to the floor number here. "Why don't I drop you off on the second [floor]?" Someone might also say, "There's trouble on three." Meaning, the third floor.