That is correct, If I go to US without an ESTA or say a country that requires a VISA or do not meet there entry requirement, it does not matter what the reasons for travel, I will be an illegal alien.
But there is fault in your logic, these people coming on boats, it's fair to say are not comming to Britian to see that sights etc, it's fair to say they are coming without any paperwork, they have not met any of our entry requirements and by illegal means. We have an asylum process which they have chose to ignore and go through traffickers