More than 700 people have been arrested since the group was banned by the government on 5 July – including more than 500 at a demonstration in central London last week.
On Saturday, Norfolk Police arrested 13 people accused of supporting the group, after a protest in Norwich city centre.
The Met added that more prosecutions were expected in the coming weeks and that arrangements had been put in place “that will enable us to investigate and prosecute significant numbers each week if necessary”.
Palestine Action has engaged in activities that have predominantly targeted arms companies since the start of the current war in Gaza.
Cooper moved to ban the group after activists from the group caused an estimated £7m of damage to jets at RAF Brize Norton in June.
The home secretary said while many were aware of that incident, fewer would be aware of other incidents for which the group had claimed responsibility.
Cooper also referenced a so-called “Underground Manual” from the group, which she said “encourages the creation of cells, provides practical guidance on how to identify targets to attack and how to evade law enforcement”.
“These are not the actions of a legitimate protest group,” Cooper said.
She also reiterated a comment made to the BBC earlier this week that some people who were supporting Palestine Action out of concern for the humanitarian situation in Gaza were not aware of the true nature of the group.