As Rand al'Thor discovered, The Boaster was a song transmitted as part of the BBC's Time and Tune series for schools, way back in the Spring Term of 1956. To help music teachers, the BBC provided pamphlets of the songs and words, for the princely sum of sixpence, so that pupils could sing along. These pamphlets are often on sale on eBay, and a quick search turned up the Spring 1956 copy, complete with views of some of the interior pages. Fortunately, one of the pages on view is of The Boaster:

Only one verse is covered, and it is the one recalled by the OP:
I'm from our village, our village,
I'm my father's son.
I've in town three houses fine.
When I've bought them they'll be mine.
The end-notes of the pamphlet reveal that The Boaster was originally published in "Children's Songs from Bohemia" published by Novello & Co. Ltd. This is sufficient to obtain the original sheet music:

So it appears that the melody is from a Bohemian folk-song (arranged by Gordon Reynolds), and the words - or poem - in the question were written by C.K. Offer. Thanks to commenter Gareth Rees, it appears that the words are a resonable, but somewhat free, translation of the Czech folksong "Já jsem z Kutný Hory" ("I'm from Kutná Hora"):
I'm from Kutná Hora,
A caulker's son.
I have three houses in Prague,
When I buy them, they'll be mine.
It is a pity, however, that we still only know one verse!