This app was mentioned in 7 comments, with an average of 2.86 upvotes
So it looks like they created this app and used the resulting data. Seems I took part a while back, without even realising.
The New York Times quiz was:
I also found an app:on Android:
https://play.google.com/store/apps/details?id=ch.uk_regional&hl=en_US&gl=US
Not sure if it's available on other devices.
Not exactly what you requested, but there's an Android app English Dialects, which has the same short English sentences read by a LOT of speakers from all over the world, including Russia.
To me you have what seems a generic southern English accent, with maybe some hints of rhoticity.
I have a friend from sirensister and her accent is the same as mine despite the fact I'm from the coastal border between Dorset and Hampshire. My accent in turn is virtually the same as a Brighton or Oxford native.
It seems the west country accent has largely died out or become very watered down in most younger people.
Try this app out it predicts where in England your accent is from. It's by a research team and contributes to their research. It goes quite deep in to your accent, it's not just a quiz.
https://play.google.com/store/apps/details?id=ch.uk_regional
Try this app and see where it places you in the UK; https://play.google.com/store/apps/details?id=ch.uk_regional it got me just about right and my girlfriend who is from overseas as from the border region
Original source and Google Drive link to original figures. The 2016 data was generated from the English Dialects app: Android and iOS.
Try this app; https://play.google.com/store/apps/details?id=ch.uk_regional took a couple of tries of saying the words aloud and it was pretty accurate