Well, the prima facie simplest approach would be to monitor channel traffic from the air, spot a migrant boat early, have a navy vessel wait for it just shy of the median line and cross into French waters to stop it before it enters UK waters, take the migrants on board, sail them back to the nearest French port, and put them ashore. I'm not a lawyer, but my understanding of the law of the sea is that's all legal since the boats are overloaded and unseaworthy, making it legally a rescue.
The biggest problem with this would be that the Royal Navy doesn't have a spare vessel. They can't even meet their existing requirements, because they spent all their money on two aircraft carriers (for which they cannot afford adequate escort vessels).
The RN, like the rest of the British Armed Forces are out of money. The new Chancellor of the Exchequer was previously Secretary of State for Defence, A position he resigned in June because of the lack of funds, and the obstinancy of the then Chancellor in refusing to increase Defence spending.
Having become Chancellor in July, he has reversed his position, and now says that there is no more money available for defence.
Basically, post-Brexit Britain is broke, broken, and irrepairable. The country is totally screwed. It's really sad.
But they have two aircraft carriers, so they can still cosplay being a world power.