I have a headcanon about the doctor’s accents, it certainly wasn’t intentional on the writer’s part but, it works.

So I’d say it’s established, the doctor’s final moments, be it speeches made by him, or the people around him, they influence the change to a degree, IE; he turned younger for Rose, eleven is more whimsical after the weight of the tenth doctor’s burdens, Vastra argues he “looked young” for Clara, the War Doctor becoming a warrior etc)

If you look at the accents for all the New Who Doctors (by the way, if you didn’t know, on average in the UK the accent changes every 25 miles):

War > 9 - Last interaction was with Clara in the Gallery in 2013 (Northern accent, Blackpool)

Nine was from the “North” (lots of planets have a north)

9 > 10 - Rose was next to the doctor when he regenerated, she had somewhat of a cockney accent (but not as exaggerated as Cassandra made it out), but certainly London accent.

Ten had an “estuary” accent

10 > 11 - Same again really, the last people he saw was Jackie, Rose, and Ood Sigma (I don’t think he counts, maybe it’s an emotional connection?), you could also argue, Luke, Verity Newman, Martha all had similar accents too and he looked back over all of them

11 > 12 - In his final moments he saw Amy Pond, the girl who waited who he longs to see, and he gets his reward in his final moments.

Twelve is now Scottish (now he can really complain)

12 > 13 - And again, he gets to see his long lost companion Clara in his final moments, a Northerner, and Thirteen speaks with a Yorkshire accent.

And then it breaks down at 13 > 14, but we don’t know what shenanigans has gone on for this to happen