
This thing which looks like a cheapo sentry box is known as a Hudd.
Hudds are portable shelters used by ministers conducting graveside services. I have put that statement in the present tense because, though I've never seen one employed, this example looks to be of fairly recent manufacture and may, conceivably, still be in service. They were introduced in the 18th century for the convenience of Anglican clergymen who didn't want to get their wigs wet.
I photographed it in All Saints, Odiham. I've seen them in other churches but they're sufficienty rare to be displayed as objects of curiosity.