Cracked vent pipe collar

WARNING: 70s bungalow. Previous owner has at some stage painted the original grey plastic piping black. Also the lead flashing! Of course it is now all flaking off and looking awful.

The soil vent pipe connects through a top hat lead slate.
I noticed a cracked rubber collar hanging loose round the base of the top hat.

I *presume* this collar should be for the top hat/vent pipe junction and has fallen down at some stage.
Question: Is this right? Or does there need to be a collar round the base of the top hat? I think not, as the top hat directs any water straight down the lead tile and into the gutter.

I have done a temporary repair (see pics) but will try one of these...
Although this collar is UPVC and the original is pliable rubber.

From the phots, you have a purposed made lead weathering 'slate' or collar. Cut away that split weathering at the top and slide down a new 110mm weathering collar and if slack make watertight with some mastic/silicone. The old paint can be removed from the lead with a wire brushing.

Thanks. That confirms I was correct in assuming that the old split collar is used for the lead/vent pipe union.
Just need to borrow a standoff for my ladders so I can reach the top of the vent pipe. The vent pipe cowl is not larger than the pipe diameter, so I should be able to slip the new one over it.