You're right that it's not the only one and remainers might overestimate the extent to which concerns about immigration affected the result but consider the following: Immigration was the
second or first most cited reason leavers themselves gave for wanting to leave despite the stigma that might be attached to such an admission. A
June 2016 MORI poll suggested that immigration was far and away the top concern of UK voters in general and stated that this concern had increased 10 points since May. Immigration was of particular concern to Conservatives, UKIPers, the 65+ and those with a social grade of C2DE - all demographics which disproportionately voted leave. The second most cited primary concern of all these groups? - The EU. Of those that cited the EU as their primary concern Immigration was their most mentioned "other important" concern. Of those that cited Immigration as their primary concern the EU was their most mentioned "other important" concern. This is, again, true of the aforementioned leave leaning demographics.
That immigration formed the bulk of the Vote Leave campaign's messaging is heavily suggested in
this Independent article. The same article also demonstrates the throughline connection between fear of immigration (the lead), the nhs, loss of sovereignty and the resulting appeal of Dominic Cummings' £350 million:
Immigration was quite clearly Vote Leave's totem of the sovereignty they were claiming we would regain.