I think the way you portray Brexit is rather telling.

There's actually a ton of very informed analysis that could be boiled down to "leaving the EU will result in increased NHS funding". Some of it is academic and wonkish, some of it is intuitive and working-class. But it's there. If you aren't aware of it that says more about how much you tried to expose yourself to such arguments, I think.

A simple version goes like this:

1. The Eurozone is an economic backwater and Brussels a monolithic quasi-socialist archetype of Big Government.

2. So, growth in the EU is terrible and will remain terrible for a long time. The UK's economy is actually beating the other big mature economies in growth, even Germany, despite Brexit related uncertainty, so there are good reasons to believe the UK has it more right than the rest of Europe does, economically speaking.

3. But in the EU the Euro is sancrosanct, it cannot be questioned and EU institutions will do "whatever it takes", to use Monti's phrasing, in order to avoid it breaking up.

4. Inside the EU the UK is a sitting duck politically. It's unpopular with other member states because it's not populated by true-blue starry-eyed EU ideological believers and tends to argue for smaller government. But its political elite feels like it literally can't leave, which means its membership fees can be set arbitrarily high and money can be and should be extracted from its economy at will.

5. We can already see this happening with the entirely political and arbitrary "exit bill", a so-called bill that's written in no treaty or legal text anywhere. The EU demand it purely because they can and they know the psychologically weak and ideologically addled governmental classes will roll over and do whatever Brussels wants. We can also see it in the rapidly rising membership fees, which are tied to GDP and not any kind of actually delivered services.

6. Thus to Remain is to signal vast weakness to the Brussels conglomerate, who will then extract as much wealth from the country as possible. In case of Eurozone recession or bank collapse the UK will certainly be called on to fund a bailout, despite all the treaties saying this won't happen. Anyone who believes that hasn't studied the EU's history: it is a dead cert thing.

7. As a consequence, remaining in the EU will drain funding from all local government services, and especially the NHS, which will be hit by a double whammy of reduced UK government budgets due to the EU taking tax revenues and becoming a free hospital for all of Europe as a Eurozone financial crisis knocks out health insurers and freedom of movement ensures the NHS can't separate Brits from everyone else.

What I outlined above is a scenario you seem to believe isn't supported by any "informed analysis", but it's not complex, or absurd, and you can read about the individual components in many informed analyses. Just search for it.

Moreover, all the above is considered obvious by the working classes. Look at the Conservative election adverts that spell it out specifically - switch to an Australian style immigration system and there will be more money for the NHS because fewer low-earning immigrants will be using it.

Obvious, innit?