And isn't the plaza, and walk through from Portland Place, under the 'arch' to the right of The One Show Studio, and entrance to the Peel Wing, and out over towards Wogan House, a public right of way?
Hence, unless the BBC got an emergency court order from Westminster Magistrates Court to ban public access (and therefore throttle the protesters) there was nothing the BBC, and the third party security staff could do.
I was down there last Saturday afternoon, and there was a protest of some sort facing BH from the steps of All Saints Church - if a boombox playing Arabic music, a large flag and a couple of banners, counts as a demonstration protest - and apart from the occasional glance by a BBC security man, all seemed happy with the protest.
My understanding is that whilst it is a public right of way, it is BBC property, and the BBC are able to close the piazza if they believe there is a safety issue. I suspect they have an agreement in place with Westminster council to do this. It's not unusual for the piazza to be closed and restricted to BBC staff and invited guests.