A-hunting We Will Go, the Grand Old Duke of York and The Nutting Girl have seen a lot of interchange of tunes over the years. When The Nutting Girl is played in sessions round here as a Morris jig (with slows) it is not unusual for all to sing over the final bars:

A-hunting we will go, my boys,
A-hunting we will go,
We'll catch a little fox
And put him in a box
And never let him go

This refrain is also not unkown to primary school children, but for them "never" becomes "then we'll"