That is not my view. At the 1million plus whoknowshowfuckinbigitwasabsolutelyhuge 2003 anti-war demo the police first said 20,000. Then 10s of 1,000s. Then agreed with Livingstone that 1 million plus was a safe bet. Then released an official statement saying 'over 100,000'!
On the G8 Gleaneagles protest they tried to ban the police then allowed a certain restricted number (3,000 or 5,000 I can't remember). They then attempted to stop thousands from joining the march saying that the 'agreed' figure had been exceeded before giving in and allowing all to march. The figure they then gave to the media was their original restricted number.
Strangely I find that Sky News tend to be more honest/accurate if they have their helecopter out to estimate numbers.
All estimates are just that - estimates. Demonstration organisers will tend to estimate optimistically. The police deliberately downplay numbers (except in their estimation of turn out to the Countryside Alliance demonstrations - wonder why!).