I'm very familiar with the English Channel in this area.
Quite some time ago, I was part of the RNLI crew on the lifeboats at Eastbourne which is to the east of Newhaven. We've been out on many, many callouts around the coast in this area, as far as Brighton sometimes to assist the crews there and including the Newhaven area, as well as recovered probably at least 50 bodies in my whole time in service from the sea.
What I would like to say regarding Anthony ending up in the water in Lewes and being taken out to sea down the Ouse and through the ferry port at Newhaven into the channel, it is a tidal river, was flooded at the time and when the tide would be receding back into the channel, the chances of him getting that far would be very slim at best. This would be because if he had passed away and drowned, he'd have sank to the riverbed almost certainly very quickly, along the river and the river bed itself, there's a large number of areas that a body could have got snagged on and held in place. By the time the body starts to swell and become 'gassed' where it would float to surface, after over 2 weeks, he would have been found I'm sure.
By now, if he was in the water, he should realistically have surfaced by now and would have been spotted somewhere.
I would place a strong bet he didn't land in the River Ouse regardless of the current, water levels and flooding. IF he did end up in the Ouse, I'd gamble on him being around Denton Island area just before Newhaven port, I'd have hoped that area was searched especially as there's quite a lot of boats moored up on the west side of the Island.
We have picked up bodies from the beaches next to Newhaven a few times that were swept to shore. We also were given the grim task of recovering a lot of the suicides from Beachy Head.
There's also the DFDS TransManche yellow ferries sailing to Dieppe twice a day, morning and night routes. He could possibly have jumped onto the 23:00 sailing that night IF he absconded. That ferry is very easy to get on without a passport.