I don't hear her as posh at all. She's got a definite regional accent though an 'educated' one. To me, posh is Cameron, Johnson, et al. Gove massively changed his accent at Oxford; he won a scholarship to my father's old school and would have ended up with a similar Scots accent to most lawyers, doctors, etc until he decided to change it.
(I sent a video of me with one of my dogs to someone last week - I was quite amused to find that after 40 years back in Scotland and 30 down south in Fife, I still have my English public school accent!
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