Are EU universities as of 2019 more dependent on external funding than 20 or 40 years ago? Is there any EU policy on increasing external private funds and reducing public funding?
They are more dependent alone due to the fact that the EU spends steadily increasing sums on research over the last decades. See the table on wikipedia.
FP9 or Horizon Europe will be around 100 billion, so another increase.
Also, just google "brexit universities britain eu funding alarm" to get some thousand articles/comments how dependent british universities are on EU funding.
My qualitative answer is based on my experience in France, I don't know if it applies to other countries. I would think it's similar for Germany, Spain and Italy at least but I'm not sure to what extent. The EU has a large research and innovation budget (currently H2020), but as far as I know every EU country is free to choose their research policy (and the amount of public spending) at the national level.
The evolution in the past 20 years is indeed quite clearly in the direction of less recurrent funding and more external funding. The major change in France was the creation of the ANR in 2005, a public funding body intended to offer grants to research teams in a project-driven and competitive way. There have been various other structural changes which affected how research is funded, in particular temporary junior positions (PhD students and postdocs) which often depend on external funding nowadays. An observable consequence of this trend is that most researchers spend a significant part of their time applying for grants, whereas this was very rare 20 years ago in most universities.
Collaborations with the private sector are also encouraged, but this is also largely funded by public money (in particular with CIR (fr) a controversial tax cut for companies to invest in research and development).