The documentary is called 'The Secret World of LEGO'. It includes a thread of the popular, just launched Bricks and Bricks Culture magazine.
Here is the synopsis from the Channel 4 website:
"Last year LEGO became the most profitable toy maker in the world. Now this notoriously secretive, privately-owned super-brand has opened its doors. We discover what makes it tick, meet some of its key people and reveal more about the company DNA than ever before.
"In The Secret World of LEGO, we follow Justin, a 23 year old design student, as he travels to LEGO headquarters in Denmark in pursuit of one of the most hotly contested jobs in the world – a LEGO set designer. We meet Liverpudlian Matthew, who undertook the same process and has now risen to become a Vice President of Design. We follow Mark and Tom, two adult fans of LEGO, as they try two different money-making schemes they hope will transform their love of the brick into hard cash. And there’s Roar, the LEGO “reputation manager”, who guides us through this secret world - until we get a little too close for comfort."
Here is the trailer: