At the risk of hijacking this thread…
To be fair (to both of them) I think May is taking the flack for the total cock-up that has been the state of Brexit negotiations since we sent the Article 50 letter but to lay Cameron’s problems at her feet is probably a bit much.
Originally I thought Cameron had called the referendum purely to silence Tory party Euro sceptics but having read a few bits and pieces on the situation I’m not sure it is that straightforward. Nick Clegg’s book is worth a read (but not a fiver, borrow a copy if you can) .
The problem, really, was that the EU was/is committed to “ever closer union” but that the UK was almost certainly not going to be comfortable with that, nor with the inevitable membership of the Euro that following that path would entail. The other issue was that one of the pillars, free movement of people - which we can see the EU will defend to its last breath - is not necessarily an unambiguously positive thing. Large movement of population from economically depressed areas of the EU to more economically favourable ones stresses the infrastructure in the destination countries, engenders resentment in the extant populations of those countries and drains the source countries of expertise and manpower.
Cameron got some important concessions but was unable to make inroads with the fundamental problems that the EU faces in terms of movement of people.
I think that he, broadly speaking, had a point in that the GBP (Great British Public) should be consulted on our future relationship with the EU but naïve in believing that the GBP could really understand the issues involved. I think he called the referendum too early (that’s political short termism for you, of course) - we should have had the impact analyses first and analysis of what sort of relationship we might have had with the EU after leaving first and then consulted the GBP.
The result is varying degrees of chaos with ordinary people and businesses, who just want some degree of certainty with which to plan their lives, caught up against the fact that we have a sort of Brexit event horizon beyond which governments cannot see, cannot provide guarantees, and certainly won’t issue any permits, documents, visas or anything else.
It’s not that HMG is incompetent (well, not in this specific instance) it’s that really, no one knows what is going to happen post Brexit and nothing has been set up yet - you can’t apply for whatever card will entitle you to stay in France if no-one yet knows what that document will be.
As for whether we will be subject to fingerprinting and photos everytime we cross the border into the EU, well, that might just have to stem from our status as a “3rd nation”. We have to accept that if we are to leave the EU then we will be treated as citizens of other nation states who are not members - it does not follow that purely because we are British we deserve some special status (much though some would like to think that it does).