Could you please explain why? How will fingerprinting people entering the country legally through registered ports combat people entering the country illegally in the back of lorries?
A fairly common thing is for asylum seekers to lie about their age perhaps to support an application. (See also, claiming they are 17 when charged with crimes so that they can face youth justice.) Some of these people have been into the country legally on student/tourist visas, and then come back and stayed illegally. If you can match someone who claims to have arrived from a war ravaged Afghanistan with someone who flew into Heathrow two years ago to study at Thames Valley Uni then you know their claim is BS.
That makes sense - although we already do this, and it's not limited to fingerprinting - includes biometric information, including iris imaging and so-forth.
You'd also be amazed at just how many people still make it over in the back of trucks. Don't know if it amounts to a majority, but talking to a few friends who drive trucks across Eurasia, pretty much every time they do a France -> UK crossing someone either sneaks, or tries to sneak, into the lorry. Common tactic is cutting the pull cord around the edge and resealing it with a lighter, or cutting a hole in the top of the canvas.
I actually subscribe to the camp of "let them come", as I don't believe in nation-state protectionism as a concept, but find the topic as a whole fascinating, from the economic level down to the human.