So here's the council's statement in full, tweeted out on the @mynottingham account (not the library Twitter)
"Nottingham City Council has cancelled a booking to use a space at Aspley Library for a talk by author Julie Bindel today (Saturday 25 June). This is due to the speaker’s views on trans gender rights being at odds with aspects of the council’s Equality, Diversity and Inclusion Strategy.
Nottingham City Council Deputy Leader Cllr Adele Williams and Portfolio Holder for Neighbourhoods, Safety & Inclusion Cllr Neghat Khan said:
“This was a private booking at Aspley Library by the ‘Nottingham Women for Change’ group and all ticket sales and marketing of the event had been undertaken independently with no input from the council.
“While it was known that the event was going to be from a feminist perspective, no information around the speaker’s views on transgender rights was brought to the Library Service’s attention.
“Once we became aware of this, we took the decision to cancel the booking. Nottingham is an inclusive city and as a council we support our LGBT community and have committed to supporting trans rights as human rights through Stonewall. We did not want the use of one of our library buildings for this event, taking place during Pride month, to be seen as implicit support for views held by the speaker which fly in the face of our position on transgender rights.”