Cambridge Dictionary says: In informal situations, we can use down to talk about a quick trip to a destination which we consider to be less central than where we are. In this meaning, we can use it with or without to. Without to is less formal:
I’m just going down (to) the shop. Do you want anything?
Are you going down (to) the golf club tonight?
Is Cambridge wrong here?
I haven't ever heard "I am going down the shop" unless used to say "I'm perusing the aisles of a store", and not "I am going to the shop."
Maybe it's different in the UK? I can't even see how this would begin to be right.
I understand that
- I am going down the store
and
- I am going down to the store
are two different things. Is there a dialect / is it "informal" to mix those two phrases into the 2nd definition?