I made no comment about her accent.
I find her tiresome and smug because, in any interview I've watched, she condescends to and patronises those on the other side of the argument. She frames everything in terms of moral superiority and she frames her interlocutor as shamefully adhering to immoral and (what horror!) old-fashioned beliefs. Her argument generally boils down to her views being superior and correct because she is nice.
Speaking as a Lefty, Thornberry epitomises everything I've come to dislike in the upper middle-class, middle management politicians who have taken over Labour. She seems to have no clue when it comes to class-based analysis or class consciousness, instead she seems to hold the full set of bien pensant views that 'naice' upper middle-class women find fashionable to hold these days (á la Stella Creasey) and if those beliefs disadvantage the less well off then so be it, as long as her fellow travellers see her as being kind.
Frankly, she gives me 'lady of the manor educating the undeserving poor' vibes.