On the contrary, I shall spend two full days climbing in the Peak District, which is handy for me as I live there.
And you aren't too far away, as you live in the Manchesters.
Given that the Peak District is subdivided into the Dark Peak, and the White Peak, is it really such a crime to use the term 'Peaks'. It would clearly be erroneous to talk of the Peaks District, but I tend to interpret 'the Peaks' as meaning the combination of Dark and White, rather than an abbreviation for the District as a whole.
I could be wrong in making this assumption, but at least it means that I can accept the term with the utmost equanimity, and happily get on with worrying about stuff that perhaps matters a bit more (to me at least).