"Hampshire" was the version I knew.

I came to this website (from New Zealand) while Googling for the phrase "calico drawers", as I wanted to see if there were any more verses to the one sung to me in 1969 on board ship going to the UK. Imagine a drunken Englishman singing this verse under the moonlight and the tropic stars, with the phosphorescence on the water, etc etc. Not quite as romantic as the occasion demanded, somehow!

Be I 'ampshire
Be I buggery
I comes up from Wareham
Where all the girls wears calico drawers
And I knows how to tear 'em.

I also saw the blackbird song printed on tourist tat in Dorset in the early 70s before the Wurzels recorded it, so it was around at the time.