> for hard Brexiteers, taking back control of the UK borders to limit immigration is a major outcome of Brexit

For some of them, maybe. But certainly not all; many of them are globalist libertarians with no desire whatsoever to reduce immigration.

A few points:

* ["Global Britain"](https://globalbritain.co.uk/) and ["go global"](https://leave.eu/trade/) were key Leave slogans.
* Only one-third of Leave voters cited immigration as their main motive in [Lord Ashcroft's exit poll](https://lordashcroftpolls.com/2016/06/how-the-united-kingdom-voted-and-why/).
* Many key Leave supporters are pro-immigration:
  * cabinet member and one-time [PM contender](https://www.thesun.co.uk/news/3761507/who-be-next-prime-minister-uk-theresa-may-resign-election-latest/) Michael Gove speaks approvingly of Britain's ["liberal approach"](https://www.bbc.co.uk/news/uk-politics-43821484) to immigration
  * other previous [PM candidate](https://www.express.co.uk/news/politics/1109085/boris-johnson-prime-minister-tory-party-leadership-contest-theresa-may-brexit) Boris Johnson has called for an ["open approach"](https://www.bloomberg.com/news/articles/2018-05-23/boris-johnson-calls-for-welcoming-approach-to-immigration), ["clashed"](https://www.independent.co.uk/news/uk/politics/boris-johnson-immigrant-amnesty-windrush-commonwealth-theresa-may-home-office-a8321046.html) with [Remainer](https://www.euronews.com/2018/12/12/what-is-theresa-may-s-view-on-brexit) Theresa May due to his defence of immigrant rights, and [called on the government to make a "liberal" case](https://www.telegraph.co.uk/politics/2018/04/18/boris-johnson-brexit-not-migration-calls-shots/) for immigration.
  * yet another [PM contender](https://www.biznews.com/global-investing/2016/06/30/brilliant-see-why-dark-horse-daniel-hannan-serious-contender-to-be-uks-pm), Daniel Hannan, the Secretary-General of the [biggest EU-skeptical EU conservative party](https://en.wikipedia.org/wiki/Alliance_of_Conservatives_and_Reformists_in_Europe), is a pro-immigration liberal who has written multiple articles denouncing Remainer claims that Brexit was motivated by a desire to restrict immigration. ([One example.](https://www.conservativehome.com/thecolumnists/2017/06/daniel-hannan-a-year-ago-tomorrow-britain-voted-for-freedom-and-here-are-three-remain-myths-about-the-campaign-that-must-be-debunked.html))

The narrative that the Brexit vote was motivated by a desire to reduce immigration is common on the pro-Remain Left, but for actual pro-Leave politicians it's often either a secondary objective or something they actively oppose. There's no need to why these people are taking positions that go against their values, because they *don't* go against their values in the first place.