Heads the police loose, tails they are wrong !
If there is evidence to SUSPECT that a person has committed a crime there is power to arrest.
OK so they could have asked Mr Cooke to 'accompany them to the police station' 'to assist police with their enquiries' etc, but in reality they all amount to arrest.
Clearly when a serious crime appears to have been committed it must be investigated. Had the police not done so in this case they would have been failing in their duty to the public. Until the facts are investigated no one can know if a crime has or has not been committed.
If Mr Cooke has not broken the law, he will be released without charge.
I really don't see what the beef is here.