Brexit was voluntary the entire way. The referendum wasn't even binding. Cameron could easily have said it was too close for a mandate to be clear. Imagine what they would say with an independence vote like that in Scotland.

The British conservative movement wanted Brexit. The real story is they almost didn't even make it over the line to 50%; they pushed ahead with something that didn't require a referendum; was obviously becoming a worse idea as the years went on; and was completely reversible right up to the moment they actually left.