I don't think it matters very much exactly how many were there. I've been on some big demonstrations: the march against the war in Iraq, the huge CND demonstration in the 1980s, an anti-apartheid one when Thatcher invited Botha to tea in the same decade. This was of a similar size.
Forgive me if I show some of the library-related placards carried by marchers. When I reached Hyde Park, I'd missed Brendan Barber and Ed Milliband. I dried my tears of disappointment, and listened to Sam West deliver a trenchant defence of arts funding, at threat from a philistine government. This government, he said, is running the country for people who can afford to buy all their books, not for the people who borrow them.
The media have latched onto some incidents, well away from Hyde Park, involving people who were nothing to do with the march. Indeed, from what has been revealed of the activities of undercover police officers, such as Mark Kennedy, it seems quite probable that among those involved in the violence were policemen.