Theresa May's UN speech, two days before the World Peace Day, preaching to UN members from all over the world that it is their "duty" to control migration flows was not very helpful for Britain's world image. Plus won;t bring any results. Few if any countries have the intent, let alone the resources, to do what she asks for.
People fleeing war or political persecution or wanting to improve their lives will continue to cross borders and go to extreme lengths to reach Britain and other "attractive" countries.
They will continue to arrive by boats to Greece and Italy aiming to reach mainly Britain or Germany.
Why is Britain such an attractive destination. I have not seen a thorough analysis of that. Brexiters will say: The NHS. Yet Germany and other countries have better systems. Maybe it is the language and BBC World!
In any case, May is promoting to the world an image that is not only not one of an Open Britain. And while many will rush to specify that a) migration of people and b) trade of goods and services and movement of capital and investment are not the same thing, many others will claim that they go hand in hand, at least in terms of image to the world.