In the Tapas 7 statements there are 3 instances of the phrase "just shut".
1. David Payne rogatory "Err and then you know the other area, the other areas I remember going into Kate and Gerry's err bedroom with Gerry and he'd perhaps you know fling a cupboard open and just have a look and, ah you know and just shut the door and you know in a vein, desperate hope that she might have been err you know in, in the wardrobe or something, and then he, you know flung him, flung himself on the floor and just you know kicking the floor and just with, you know, she's gone, she's gone, err and then as I say, I, I, after that I can't really say exactly, you know. "
Here he is talking about a wardrobe door.
2 and 3. Next two from J Tanner rogatory "Reply “Erm well you couldn’t, I doubt I dead locked it cos the door’s, if you just shut the doors they locked anyway, erm so nobody could have got, if, if it was the door, if it was the road side door, if you shut it, it locked but you could further dead lock it, erm so no I doubt it, I think I would have just shut it, I don’t think I would have dead locked it”."
I think here she is describing the minimalist thing you can do to the front door "just shut it" but she does not say what action makes that happen. It is not "just push it shut". The way she links that with the possibility of dead locking the door I suspect the use of the key.