How can it be rational?
A person who supports the UKIP because they don't want immigrants to come to the UK is basically saying that the 60 million random strangers that he has never met who currently live in the UK are acceptable to him, but a few tens of thousands more random strangers he has never met will cause a problem.
That's a fundamentally insane position to take.
That's an unreasonable claim, three times over.
First, no, all such a person is saying is that a few tens of thousands more random strangers he has never met will cause a problem. Opposing immigration in no way involves saying the 60 million random strangers who currently live in the UK are acceptable to him. At least a few tens of thousands of the random strangers currently living in the UK will also cause a problem. However, there appears to be no practical way to get the tens of thousands of immigrants who will cause a problem to go home. And in addition, there are at least tens of thousands who will cause a problem who can't be sent home because they already are home. That makes three problems the UK has. Two of them are not solvable. But to infer "When you have three problems and you can't solve two, trying to solve the third is a fundamentally insane position to take." is a fundamentally insane position to take.
Second, while I recognize that you have long been sounding like you think ecological concepts like carrying capacity don't apply to H. sapiens and anybody who values low population density is fundamentally insane, that's a whole separate debate from your contention that there's a contradiction between accepting those who are in the UK and rejecting newcomers. For purposes of the current thread, you don't get to take for granted your counterintuitive conclusion that there's no such thing as overpopulation. We are not talking about a few tens of thousands more random strangers. We are talking about a few tens of thousands more random strangers
this month, plus another few tens of thousands more random strangers next month, plus every month into the foreseeable future. Three hundred thirty-six thousand more this year, a million more in three years, ten million more in thirty years. Anybody who thinks Britain is already overpopulated or close to it is perfectly entitled to regard the one-month shutter speed you choose to limit your mental photograph of immigration to as an arbitrary and thoughtless exercise in "Look how much straw the camel is already carrying; one more straw obviously won't make a difference.". True, this month will probably not be the month that tips Britain's population density over the edge from acceptable to unacceptable. But insisting that others ought not to think further ahead than one month just because you won't is a fundamentally insane position to take.
And third, the contention that it's insane to regard new immigrants as unacceptable and current residents as acceptable appears to rely on the premise that there are no statistical differences between the immigrant and resident populations that would tend to impact their acceptability. That premise is an article of faith; you don't have a reason to think it's true. The percentage of people currently in Britain who are already up to speed on living in a way that doesn't impose substantial negative externalities on their neighbors is not necessarily equal to that percentage among the candidates for next month's few tens of thousands more random strangers. To consider it irrational to fail to take it on faith that those percentages are equal is a fundamentally insane position to take.
... No restrictions on movement of people whatsoever? All people would need to do is turn up at a welfare office and demand welfare?
...
Freedom of movement need not entail the right to claim welfare at one's destination.
Not everyone is entitled to welfare where they are; why would you imagine that they would be where they are not?
Um, for the painfully obvious reason that the same phenomenon that causes border controls to go away is also what causes immigrants' welfare claims to be honored: government power falling into the hands of ideologues who think it's racist to pursue the best interests of their country's citizens. In some alternate universe where freedom of movement were happening because government power had fallen into the hands of radical libertarians who abolished welfare, you'd be right. But this isn't that universe. This is a universe where radical libertarianism appeals to 2% of the electorate and the people pushing open border policies are primarily multicultural nihilists.