As Mull says, the problem lies back in whichever country they originate, but that's not somethign we can sort out easily. Why do they choose to try and come to the UK? I know some do go elsewhere.
Presumably they see the UK as attractive - we take them in, we given them shelter, we give them money, we give them jobs (even at minimum wage it's a lot more than they get in their own countries so must make them feel quite rich).
So ... there's (to me) a fairly simple answer - we stop welcoming them in, we stop giving them shelter, stop giving them money, stop giving them jobs - don't make it such an attractive proposition to risk lives getting here.
After all, we have a crumbling National Health service that is in desperate need of our money.
I am not criticising foreigners who come here and have the skills to do jobs - doctors, nurses, etc. The ones I am criticising are the ones that are hell bent on breaking whatever laws it takes to get here, who are causing major disruption to the economy of this country, then expect (and get) looked after.