Fox on 29th May 2016 said it was "entirely possible" to meet the pledge to reduce immigration to tens of thousands. "But only in my view if we left the European Union," he added. Daily Mail (Fox was a well know Tory supporter of Leave)
Gove and Johnson said migrants will be barred from entering Britain after a Brexit unless they can speak good English and have the right skills for a job, and proposed a points-based system. Telegraph (Gove and Johnson were seen as the leaders of the Leave campaign).
Hoey said that Brexit would decrease the numbers of low-pay immigrants from EU countries the heat. Hoey is a notable Labour Brexit campaigner.
In general all Brexit supporters said there would be a decrease in immigration following Brexit. It is implied that there may be some greater immigration from non-EU countries under a points system.