the royal navy has already been tasked with patrolling the English channel... they have announced that this operation is being scaled back because they cannot spare the vessels...
https://www.thenationalnews.com/world/uk-news/2022/08/16/royal-navy-to-end-channel-migrant-patrols/?outputType=amp
it is not accurate to claim for certain that the migrants crossing the channel are not refugees... there is very little recent information available on this subject but a proportion of them do in fact claim asylum when they reach the uk... this is something they have every right to do. It is also at present the only way to claim asylum in this country due to a decision by the home office to refuse all applications for asylum made from outside the uk.
the result is that genuine asylum seekers and organised criminals make the crossings illegally at the same time... the former used as a smokescreen by the latter. As a result of our own policy we cannot process applications anywhere else but here.
towing the boats back to france is a non starter as uk vessels would need to enter french territorial waters for this purpose... they are not going to permit that in a hurry.
the most sensible solution is to process applications for asylum in the uk, in the north of france. This would allow a safe and legal route for asylum seekers and deprive criminals of their smokescreen.