At the end of the day it is purely a French and EU problem for what are for the vast majority economic migrants. UN refugee international law is that when fleeing a dangerous country you register in the first safe country you come to and claim asylum. This means that the majority should be in hostels or camps in Greece, Italy or Spain in limbo for a year or two while their application is processed. If their application is successful they will then become a Greek, Italian or Spanish citizen and are free to settle in any EU country. If your application is unsuccessful then you will then be in limbo while appealing and awaiting deportation back to your country of origin. In reality you are unlikely to be deported, so will be in a state of limbo.
Now if you are an economic migrant you have a very different motivation. Once you land in an EU country, you start your migration to where you want to go as quickly as possible, taking advantage of the EU open borders and disappear into the black economy or apply for asylum there hoping you can legitimize your work documentation and make more money. Your country of choice is normally based on four things: You can speak a smattering or more of the local language, other friends or family legitimately or as economic migrants are all ready in the country, the country is rich so there are more rich pickings to be had or wages and job prospects are good. The UK scores well on each of these. This is why they shun France and congregate at the Channel ports, trying to break into any vehicle they can use to get them to the UK or if you have enough money left paying for one of the 'unofficial small nightly ferries' that will take you to the UK. Once here you can enter the black economy or claim asylum with no documentation claiming you washed up on a beach and this is your first safe country. In either event it is very unlikely you will ever have to leave.
Nobody knows how many illegal immigrants there are here? Government estimates are at least 2 million. Some combined supermarket food sales figures suggest maybe as high as 15 million. I suspect it is somewhere between the two.