Because the reality is numerous studies (well, those from impartial organisations) have shown immigration is of net economic benefit to the UK, and not one single prime minister would ever be willing to create a situation where we go into recession because we've decided to cripple a number of industries just because of a bunch of blame gaming.
Migration to the UK was already controllable for migrants coming from outside the EU, and we already had a points system for those people, and yet, more people still migrate from outside the EU than inside, despite the propaganda meaning that even where we could control immigration we can't and wont. IIRC the most recent figures showed something like 272,000 migrants from outside the EU last year, but only about 236,000 from inside. If we really wanted to we could've cut immigration in half by just banning migration from non-EU sources already, but we don't and wont, because we need things like scientists, doctors, nurses, teachers, fruit pickers, and so on and so forth because no one here wants to or can do those jobs.
This is precisely why so many top Brexiters fled with their tails between their legs when they won the vote - populism is such an easy politics to get people onside because humans mostly appear to love being angry, so pick something to get them angry at and they'll rally around you. The difficult bit is if you win you then have to somehow square your populist lies and blame gaming with reality - this is also the problem we now have by way of increased racism in the UK. Politicians like Farage put so much effort into blame gaming and demonising minorities that hate crime is massively up, and an MP even got killed in the run up to the referendum.
Note that I'm not trying to generalise here, migrants are not a net economic benefit to every country - the number of Syrian migrants seen in some European states and the lack of the lack of suitable jobs for them, as well as migration into the US do result in net costs, it's just simply not true of Britain where they're net contributors.
Of course there are more than economic arguments, talk of integration (though I don't buy those personally - violent football hooligans born and bred in Britain also don't integrate, it's not a migrant specific thing, some people are just assholes), but economics is at the core of a politician, particularly a prime minister's calculations. No PM will ever put themselves in a position where they have say "Guys! I fixed the immigration problem, but yeah, your grandma died because we ran out of nurses, oh and taxes are going to have to go up to make up the shortfall in income to pay the police too. We're also out of carrots for Christmas this year, no one to go and pick them.".
Technically though yes, as an island, there's nothing to stop us from physically locking down our country as such, though even then people will smuggle across to some degree.