Three quarters of Asylum claims are granted, so it won't do to dismiss 'these people' as either 'illegals' or economic migrants. If you are coming from countries accepted as unsafe (Afghanistan, Syria, Somalia for example) that percentage rises massively. Likewise if you are coming from India or Vietnam (for example) you are highly unlikely to be granted Asylum.
Most Asylum claimants aren't coming from France by boat, they are arriving by air and UK is the first safe country reached.
Of course there are also would-be migrants attempting to reach UK to escape poverty, climate change or other natural disasters. They aim for UK because of the English language, just as West and North Africans tend to gravitate toward France and South Americans aim for Spain. If they can't substaniate an Asylum claim they will be removed from UK.