Maybe he got washed out to sea, it's the divers responsibility not the rescue team for his disappearance.
By the report quoted he was already mid Channel when he went missing. You can’t get ‘washed out to sea’ from the middle of the sea.
In what circumstances is a disappearance the responsibility of a “rescue team” ?
There seems to be considerable confusion on this thread about how done, certainly in this part of the world.
What happens is a bunch of people (up to 12 depending on the boat) go out to some site of interest. That site is ANYWHERE in the wet bit between England and France. Then they jump off the boat, head down a rope and hope to find a wreck at the bottom. After a while they are expected back at the surface and are collected by the boat. Mostly you can’t see the coast.
That wet bit is subject to the actions of the moon and the sun, so the wet stuff moves back and forth. In addition lots of large cargo ships are heading up and down.
So what if someone doesn’t reappear? You ask the passing huge ships to keep an eye out (although they are unlikely to notice something as small as a dive boat, let alone a diver) you get a helicopter out and any lifeboats. You have a look for a bit, taking into account which way the tide was running since the diver got into the water.
One of two things can have happened, either the diver surfaced or not. If they surfaced then you hope to find them. That sometimes happens, with divers being found after 8 hours. On the other hand it is quite possible that they are lost on the bottom. How long do you look? In places with less tide I have known searches go on for days, but in that particular area they will be long gone.
These dives can have particular complications, getting back to the surface isn’t the end of it.