Alternative for wickes PVA glue in america
PVA is one common type of wood glue (one global example is Gorilla wood glue), though the product in the video is the cheaper builder's PVA which can be mixed into plaster, or diluted and used as a primer or dust-reducing coating for concrete.  I'd expect it to be a little thinner than PVA wood glue, but the latter can be diluted with water.  PVA is sold as white glue (Home Depot), but go by the formulation not the colour.

You can buy PVA primers as well, or even a lot of kids craft glue, but having watched a little of the video I suggest just using a PVA wood glue (ideally one sold for interior use only as you want a little tackiness).  The kids craft glue tend to be thinner as well.  

PVA glues are largely interchangeable (though in some cases some are stronger, and you don't want too much water in many woodwoodworking projects)