I have an American version from an Ed McCurdy album that mentions the 'beaver hat' and has a 'bow (or bough) down' refrain, but it is different from what you have posted. The first bit goes:

There lived an old lord by the northern sea
Bough (bow) down
There lived an old lord by the northern sea
The boughs they bend to me
There lived an old lord by the northern sea
And he had daughters one, two, three
I will be true, true to my love, love, if my love will be true to me

A young man came a courting there
Bough (bow) down
A young man came a courting there
The boughs they bend to me
A young man came a courting there
His natural choice was the young and fair
I will be true, true to my love, love, if my love will be true to me

He gave this girl a beaver hat
Bough (bow) down
....

--Stewie.