ahremk's query reminded me, I've had this vase sitting round for a couple of years.
It is the same height and width as a piece on Hardernet.dk (great site, Peter!): the 70th entry in the Lütken, Per kunstglas solo section. But it's very heavy - around 900g instead of the stated 628g. It's smoke grey colour, has a flattened top rim, and has a ground-out punty mark on the base. No signature.
Could it be by Lutken? I've always thought it might be, but this is the first documentary evidence of anything remotely resembling it.