Scrump, the traditional White Hare is not lost. We have one version of it here. Seth Lakeman's song is a completely different song.

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I'll copy paste lyrics here as folkinfo (and the Annexe and others) are down at the moment.

Near Howden town, near Howden town, as I have heard them tell,
There once was a white hare who used there to dwell;
She's been hunted by the greyhounds and beagles so fair,
But ne'er a one amongst them could come near the white hare.
With my fol de dol, etc.

When they came to the place where this white hare used to lie
They uncoupled the beagles and began for to try;
They uncoupled the beagles and beat the brush around
But never a white hare in that field was to be found.

It's Jemmy the huntsman and Tom the whipper-in
Go look in yonder fernside and see if she be in;
With that she took a jump, boys, and fast away she ran,
"It's yonder she is going, don't you see her, gentlemen?"

The footmen they did run and the huntsmen they did ride,
Such halloing and shouting there was on every side;
Such halloing and shouting I ne'er before did know,
As though she had been running all the time through.

The huntsmen and the footmen they all drew nigh,
Thinking that the white hare was going for to die;
She slipt out of the bush and thought to run away,
But cruel were the beagles that caused her to stay.

'Twas twenty good beagles that caused her to die,
There was not a one amongst them above a foot high;
The number of dogs there's not to be found,
Nor ever better hunting upon the English ground.

Source: Kidson F, 1891, Traditional Tunes, A Collection of Ballad Airs, Oxford, Taphouse and Son