Ah, I think we might be getting somewhere. If I load the HTML produced by Markdown into an HTML editor (GWrite) some extra code is inserted automatically, see the codebox. This does import to Calibre and convert to MOBI properly. So at least I have a work-around.
Code:
<!DOCTYPE html>
<html>
<head></head><body><p>Before the Roman came to Rye or out to Severn strode, <br>
The rolling English drunkard made the rolling English road. <br>
A reeling road, a rolling road, that rambles round the shire, <br>
And after him the parson ran, the sexton and the squire; <br>
A merry road, a mazy road, and such as we did tread <br>
The night we went to Birmingham by way of Beachy Head. </p>
<p>I knew no harm of Bonaparte and plenty of the Squire, <br>
And for to fight the Frenchman I did not much desire; <br>
But I did bash their baggonets because they came arrayed <br>
To straighten out the crooked road an English drunkard made, <br>
Where you and I went down the lane with ale-mugs in our hands, <br>
The night we went to Glastonbury by way of Goodwin Sands. </p>
</body>
</html>
Many thanks, Nick.