A West Yorkshire accent is so very different from my Central Scotland accent, and, for that matter from a Cornwall, Somerset, Newcastle, hinterland Aberdeenshire, Welsh, some London accents, but I'm managing to follow. The Doctor is speaking in express mode but it's probably the effects of regeneration.
The same problem of accents comes up with many shows. Some/many? British viewers can have slight problems understanding some words and expressions or accents on American programmes. Or, recently, we've been watching a NZ cop show, Brokenwood Mysteries, and the lack of, and weird, vowels, sometimes makes for a "what was that" moment. Same with Mystery Road, the Aussie noir. At times it wasn't easy to get all that was being said at the start, but as these shows went on, our ears became accustomed to the accents.
I think as viewers become accustomed to Ms. Whittaker, you'll start to understand and enjoy her lovely Yorkshire accent. I do already.