Driving/Getting the Learner's Permit from DVLA

I'd ring them up and ask if I were you. They just might make exceptions for people in unique circumstances like yours. At any rate, it's worth a try!

I seem to remember someone who couldn't be without their passport going in person to the DVLA office in Swansea.  A big hassle but maybe an option?

I went into the office; they still took my passport.

So you know........

She carries both British and American passports, and acquired her first driving licence in the US Virgin Islands, as it was easier to qualify there, thus allowing her to drive in both the US and UK.[5]

Who this? Answer, Actress Sienna Miller

I was able to go to the DVLA office in Beverley to apply for my provisional.  They took my passport and my US DL.  I paid the £50 fee and that was it.  I received my DL & my passport back in a few days and my provisional DL soon after... or vice versa.

But yes, if you have a US DL then you will have to take both the theory & the practical.  And I would heartily recommend getting the AA's theory guide app for the phone and hiring an instructor to help you know what to expect when taking the practical.  I know it helped me... and I still almost didn't pass my first time!