Sections 3 and 4 of the Act enable a police constable to give written notice to an organisation that a particular statement they publish electronically is unlawful, because it relates to terrorism. If the organisation does not remove or amend the statement within two working days (only Saturdays, Sundays, Bank Holidays, Christmas Day and Good Friday are excluded) then it will be considered to have endorsed the statement and thereafter be liable to prosecution for encouraging terrorism or disseminating terrorist publications.
An organisation served with a notice is also required to take all reasonable steps to prevent future re-publication of the same or similar statements. Since the law is brand new, it is not clear how "all reasonable steps" will be interpreted, but it seems likely to require at least an investigation into who published the statement and removing that person's ability to publish in future.
The Act can be found at:
The relevant part of the Act is at:
Parliamentary debate from February relating to this section of the Act: