The term used here is "street weapons", or more literally "street combat weapons". This is designed to include nunchakus, batons, brassknuckles, slingshots, chains, etc. But to make sure they didn't miss anything, they gave it a name and included anything that could be used as a weapon. So cricket bats and pool cues are also included.
In the UK, it seems the term is, as you say, "offensive weapons"
http://www.opsi.gov.uk/acts/acts1996/Uk ... 60026_en_1
But that law seems to only include knifes and edged weapons, but the law is a bit murky since it is seems it's enough that it's "offensive".
An Act to make provision about persons having knives, other articles which have a blade or are sharply pointed or offensive weapons; and about selling knives or such articles to persons under the age of sixteen years.