It looks like the idea that few claim asylum in Italy and France is very wide of the markI doubt that France has any accurate idea of how many arrive from Italy as there are few border controls, if any, as they fan out and transit to other European countries. It seems that few claim asylum in Italy or France.
Migrants crossing to England in boats are conspicuous and easily identifiable and counted.
As for housing them in detention or after being granted leave to stay, we are already releasing criminals early due to lack of accommodation. Maybe we'll also end up putting the crims in hotels.
Asylum applications - annual statistics - Statistics Explained
The latest statistics on asylum applicants in the EU are presented.
ec.europa.eu
Hopefully faster processing should reduce the numbers housed in hotels. Of course if they are successful they then need housing somewhere we need that big push on building.