Roof Void

[horseshoes]

Some years ago we had some work done which resulted in the old roof now existing under a new roof as a roof void (I hope this makes sense) We have a little sort of trap door and just use to store suitcases etc. It abuts an exterior wall from the house next door. It is icy cold in there and a huge draught comes through the little door. I've tried all manner of draught excluders. I know there is some sort of insulation board in there.There is also lagging on the floor. What else can I do? There's not really standing room in there. It's like a triangular shape.