Is this likely to be a slither of old intumescent material, asbestos, or both on these old doors.

I understand they used to put asbestos in the core of doors, this door is potentially as old as 1988.

Anyone else come across this, seems to be just behind the lippings, apart from on the top where it's exposed, perhaps from when the door was shot in, or made this way.

Its likely to be intumescent strip, c.1988 would be right for this. Its purpose is to enhance the fire resistance performance at the gap between the edge of the door leaf and the reveal where it meets the door frame. https://www.ifsa.org.uk/