The Criminal Law Act 1967 introduced the category to replace the ancient term felony.
That Act had been superseded by the Police and Criminal Evidence Act 1984, which over the next two decades was itself significantly amended to increase police powers of arrest, relating in particular to entry, search following arrest and to custody.
In England and Wales, the category "arrestable offence" ceased to exist with the advent on 1 January 2006 of the Serious Organised Crime and Police Act.
The question now for police is whether it is "necessary" to arrest the relevant person, by reference to various broadly-drafted statutory criteria.
The powers to arrest under the 1987 Order were replaced by near-identical criteria as for England & Wales.