Hmm, interesting. Looks like an inverted cone. Is it brick lined? It is difficult to get the scale. And I assume that the north facing bit is important. So, something to do with an ice house?
Well done Pete, you have it spot on. It is the interior of the ice house at Battle Abbey.
The door faces north so it is always in shade, to minimise the amount of warmth let in when the door was opened.
I worked it as I was typing my reply. It was when I thought about the significance of the north-facing door. A quick trip to google for ice house in Sussex and...