In reply to llechwedd:
> I think there have been failed attempts at introducing them to the Lake District, but I don't have details.
> I'm aware that, in Snowdonia, about a century or more ago, they were also failed introductions of them, by the Penrhyn Estate, onto the Carneddau.
Thanks for the useful reply.
I gave it a quick google and came up with an article about mountain hares in northumberland. It seems that they can still be found on the cheviot, so maybe we need to think again about the perception of 'only in the Peak'.
http://www.nhsn.ncl.ac.uk/interests/mammals/mammals-north-east/mountain-har...
Also, confirmation of failed attempts at introduction..
''In England and Wales it is known to have been introduced in the Peak District, Snowdonia, the Lake District and the Cheviots, though other than the Peak District all of the introductions are supposed to have died out (Hewson and Yalden, 1995).''
So it seems unlikely that they survived in the Lakes, but no-one knows for sure.