They do. But by design the Leave campaign tried to fudge it and use this as a strategy precisely because, whilst immigration was a key reason, it also couldn't win the vote on its own.
On a vote which was supposed to be a binary single issue - rather than an election - this is much more problematic.
It essentially kicked the can down the road and didn't give an answer to a binary question for that reason! It just left the mess for others to sort (spoiler, they didn't and still haven't for all the talk of 'get brexit done' and 'oven ready Brexit').
The referendum was also (technically) advisory, rather than binary. It didn't HAVE to be followed. There could have been a viability study which then came back and said this was a problem and that could have been used as a negotiation strategy with the EU in a different way.
Certainly we didn't have to trigger Art50 in the way we did, which put us (not the EU) at a massive negotiating disadvantage compared to the EU).
Then there was the point that since Leave did not lay out a manifesto May COULD easily have said we should leave on much softer terms then she actually proposed which would have been less divisive and would have had more broad support. Instead she shocked even the right of the Tory Party, who weren't expecting the tone and content of the October Speech.
Certainly polling after the referendum did have many remainers who would have supported a soft exit in order to fulfil the advise of the referedum. And many leavers were never in favour of a hard brexit either. So we could have gone down a consensus building Brexit, but May burnt that bridge so early on, there was no roll back on that.
This ALL directly related to the fact that there was NEVER a consensus nor majority over Brexit was because it was a hodgepodge of disparate views which were at times totally contradictory and at odds with each other.
No one could deliver a Brexit which resembled 'what people voted for' for this reason. It was a nonsense idea. No one bothered to try and do consensus building politics - instead they went at it like a hammer to produce diversive politics.
It was fucking irresponsible and poor governance which served individual careers and agendas and party political factions but did nothing in the name of public interest.
I stress in this context that it WAS NOT just the Tory Party who were guilty of this.