Crater Lake in the Lake District?

 I found these interesting striped rocks just below Combe Door on Glaramara.

They reminded me of these rocks I found in Adam-a-Cove on Crinkle Crags.

I know that the rocks in these parts were supposed to have been laid down as sediments of volcanic ash at the bottom of a lake in a caldera. So how big was the lake? On the map, there is exactly 4 miles between the sites. That would be heading for the size of Crater Lake in Oregon. The caldera on Mount Teide on Tenerife is 7 - 12 miles.