Yes, Danny has identified the issue correctly.
Making the assumption that some people voted to leave because of immigration (which they were perfectly entitled to do and should not be vilified for it) the problem was that some 450m people had the unconditional right to settle in the UK. They didn’t need permission. Since the scheme to allow those EU citizens already here to remain was launched, something over 5m applications have been received. The government expected around 3m. More than that, it is thought that up to 3m more may be here but have not applied for leave to remain (hence the calls to extend the scheme’s deadline). So that’s 8m people, give or take, that the government did not know were here and who had made no application to arrive or stay.
By contrast, some 10,000 have arrived in rubber boats this year. Whilst this is outrageous and needs addressing, it is but nothing compared to the 8m who settled legally – a figure that would certainly have increased. People have been arriving illegally into the UK from France for decades and doubtless people who were concerned about immigration when they cast their vote were concerned on both counts. But their votes meant that something could be done about the far greater numbers that were arriving by Ryanair and Easyjet.
Nobody who voted to leave expected illegal entries to cease. That problem had nothing to do with our membership of the EU. It was exacerbated by the EU's ludicrous Schengen Agreement which allows illegal migrants the freedom to roam all over the Continent once they had gained a foothold.