It was either part of Lot 49 or Lot 50, which contained a number of costume pieces from Resurrection Of The Daleks, including body suits, belts, jackets, helmets and the cap.
Bonhams auction in 2011.
I am not 100% sure if this is the same hat - there were many made for the story so it could be one of many.
Still, the seller has provided some great detailed images of the hat, giving some clues to its construction.
Resurrection Of The Daleks
Prison ship soldier’s hat
This is a genuine (not replica) cap from the classic episode of Doctor Who- Resurrection of the Daleks. It was worn by the soldiers who boarded the spaceship.
This was bought from John Fitton (RIP) Books and Magazines c. 1990, folowing the selloff of costumes from the BBC.
Not sure how to price this. It originally cost me £75, and that was quite some time ago. So open to offers. Buyer is welcome to inspect in person before buying, but cash only for collection (Surrey) please.
If you have any questions, please do ask. I have a number of harder-to-find Doctor Who items up for auction, so please do take a look and see if anthing takes your fancy.
Set Blueprints (signed by Peter Davison)
THIS IS A VERY LARGE PIECE AND DIFFICULT TO PHOTOGRAPH. IN EXCELLENT CONDITION. THERE IS SOME PAPER LOSS TO THE RIGHT HAND SIDE, BUT THIS DOES NOT DETRACT FROM THE ITEM, WOULD LOOK GREAT FRAMED.
COMES COMPLETE WITH A PROP MASTERS CERTIFICATE OF AUTHENTICITY.
SIGNED BY THE DOCTOR HIMSELF PETER DAVISON. I OBTAINED THIS AUTOGRAPH PERSONALLY FROM PETER WHEN HE ATTENDED A CONVENTION IN NOTTINGHAM, AND THEREFORE GIVE A 100% LIFETIME MONEYBACK GUARANTEE AS TO ITS AUTHENTICITY
A VERY DESIRABLE AND UNIQUE PIECE, SIGNED BY AN ORIGINAL DOCTOR.