I don't know if it will cause more countries to leave, but the EU has certainly behaved appallingly over the last few days.
As he says at the end (he is French): And for Europe to say they are going to control exports is the contrary to what they said a few months ago, that they were going to give access to everybody
The EU are not used to this much scrutiny, their systems are slow and beaurocratic, they negotiated the price down, and now they're trying to blame the British. Nice. They haven't even approved the British drug yet, that they are complaining about not getting enough of!