Just listened to the lovely Mary on Women's Hour talking about this. She was as explicit as it is possible to be on Radio 4 at 10.00am about the exact nature of the abuse she received, and even I was shocked. And that's fucking difficult to do.
How very DARE any woman have the temerity to appear in her natural unadorned state on TV when she's obviously Past her Best and doesn't even try to hide it? 
Anyone would think she doesn't Give an Actual Shit about whether the Menz (or the stupid women) think she looks hot or not??
It's the blatant lack of approval-seeking behaviour that so deeply offends men, the flagrant breaching of codes of accepted female behaviour that terrifies women. Mary has stepped outside the boundaries and ironically enough, she is seen by other women as 'letting the side down' by being in her 50s and not scrubbing up like Nigella.
And FWIW, i don't see anything wrong at all with an historian putting forward her views on something like immigration, they are trained to take a Long View of the Bigger Picture after all! The fact that she's a middle class professional would equally rule out 99% of all other Meejah Pundits from having a valid opinion either.
It never ceases to amaze me that academics, (and female academics in particular 
) who have made a career out of finding things out, analysing the facts and then presenting informed opinions are invariably dismissed as living in 'Ivory Towers', while the Bloke Down the Pub and the Man in the Street are deemed to be the founts of all wisdom and common sense.