No leading Brexiter has problems with goods, services, and capital flowing freely. They even want to leave the “protectionist club” EU, even though part of the leave-vote in deprived regions has been caused by the capital exodus that replaced local industry with imports. I will nevertheless focus on the leaver-“concern” people.
The borders of any island are “controlled” by the departure- and arrival- (in case of expulsion) approvals of countries across the water. In a rule-based order, e.g. the EU, other countries execute the UK’s wishes, and thereby underpin the widespread national border-controllability-illusion. The growing refugee-crisis should make the contingent nature of these conventions abundantly clear. Turkey, Jordan, Lebanon, Libya, etc. will not absorb Millions of people forever. Ironically, an island-mentality impedes the realisation that the continent’s physically enforceable land borders are much less reliant on international rules than UK beaches.
Leaving this aside, border control has a pull and a push-aspect: attracting people you want and repelling the others. Brexit certainly has not helped the former, but let us focus on the latter which is widely regarded as the problem at hand.
To inspect the effectiveness of push-strategies, it is instructive to look at non-EU immigration: Despite official hostility, barbaric retentions, unjustifiable expulsions, inhumane income thresholds, asymmetric legal recourse, nonsensical student-counting, and arbitrary quotas, the Home Office has consistently missed its target. The absence of a civilised, sensible, and effective immigration policy where “full control” already exists, is quite remarkable. There must be strong economic and social forces at work that dwarf the means of a committed Government.