If you're lucky, there will be a copyright notification printed on it somewhere. If you're not, you can only hope they formally registered it, and in a way that enables you to find it in the registry's database.
Medieval Times most likely holds the copyright, unless their agreement with the designer specified otherwise; as a corporate work, it would be protected for 95 years after its creation.
The original Lord Kitchener poster is in the public domain; copyright protection expired 70 years after the death of the artist, that is 2003.
Rights are likely still controlled by the BBC.
There are several entities by that name, but most are registered trademarks.
I would assume Richard O'Brien still holds the copyright.
Yes; the poster in its entirety, as well as individual elements such as photos making up the poster, are protected by copyright. In addition, there may be trademarked elements ranging from the film title to the Dolby logo.
Unless other arrangements were made, the creator is the initial copyright holder.
Warner-Tamerlane.
Muppets, Inc.
Unless other arrangements were made, the creator is the initial copyright holder.
The Richmond Organization.
The Rank Organization.