As far as I can tell, there are dozens of aerospace companies and contractors, which partner with various space programs around the world to develop, build and maintain space vehicles.
Are any of the non-US based aerospace companies and/or contractors actively, and with any noticeable actual progress, independently (or in partnership with other companies/governments, but with a non-government company or organization in the lead) pursuing manned space flight or exploration?
The only one that I can think of is Mars One that is Netherlands based and plans to establish a permanent human settlement on Mars by 2023. From their front page:
A reliable surface habitat will be set up before the first crew lands; more settlers and cargo will follow every two years.
Our plan is realistic because the technology needed already exists and can be purchased from the private space industry.
The first footprint on Mars will fascinate and inspire generations; it is this public interest that will help finance this human mission to Mars.
I'll leave it to readers to decide how realistic this project really is, but it does fit the bill based on your question's requirements. It is not government funded, and it isn't US based. As for actual progress, I'll let you be the judge of that too, their planned roadmap is published here.
One that comes to mind is Copenhagen Suborbitals, a Danish non-profit aerospace organization that has constructed and launched several privately built rockets.
Their homepage is http://copsub.com
Wikipedia has a good write-up at http://en.wikipedia.org/wiki/Copenhagen_Suborbitals
You can also find them on YouTube - search for "CphSuborbitals"
I'll admit that the manned aspect of the following program is fairly tangential to its main goals, but it is something, and the company could become a major player in the SSTO market within the next decade or so.
I'm talking about Reaction Engines. They're an English group primarily concerned with the Skylon spaceplane. It's original design was unmanned, but there have been some side efforts to put a passenger module in the payload bay. It's unclear as to whether the craft would still be autonomous; I would think so because there would be a massive design challenge to make it pilotable.
From their website:
Reaction Engines Ltd ('REL') is a privately held company located in the United Kingdom and was formed in 1989 to develop the technologies needed for an advanced combined cycle air-breathing rocket engine class called SABRE that will enable aircraft to operate easily at speeds of up to five times the speed of sound or fly directly into Earth orbit.
According to Wikipedia, the group aims to have the first test flights in 2019.
Some of the company's other projects include the SABRE engine and the group's LAPCAT design. Wikipedia goes into some detail about their entrance in that (called the A2), but I can't verify that information from the company's official website. The A2 would definitely be manned, but it would not be capable of even sub-orbital flight, nor is it designed to do that.
