Turnout was about 72%, so really it was (approx) Leave 37%, Remain 35%, Don’t Know/Care 28%.
Also worth pointing out that the hard Brexit we got, where we left Schengen and abandoned much of our cross-European programmes, was almost unthinkable, and not seriously considered by the media. Whenever it was brought up, it was decried as “project fear” by those who pushed for it.
UK was never part of the Schengen area, there was only cooperation in the form of information exchange and similar.
I don’t think the UK was ever in Schengen (at least as far as my visa was concerned). That is one bright spot here. Traveling to the UK is much easier than travel to Europe for much of the world. The UK allows for paying for QoS so you can pay a large fee and get a visa soon or a much smaller fee and get one in two weeks. By comparison, Schengen visas from all participants are granted equitably by fee and the wait time is months.