It would appear that they were threatened with even more drastic measures.
Brokenshire suggested that the government was also pushing for a "code of conduct" for internet service providers and other internet companies, which might include changing search algorithms to downgrade "unsavoury" content in internet searches.
Google told the FT that while the Home Office had been given these new permissions, the company still retained the right to decide whether they ought to be removed or not
Seems like an expedited version of the normal flagging function.
Brokenshire suggested that the government was also pushing for a "code of conduct" for internet service providers and other internet companies, which might include changing search algorithms to downgrade "unsavoury" content in internet searches.