Even if you launch a boat on a navigable water, this doesn't mean you have the right to fish from the boat. For example, I occasionally fish the Yorkshire Ouse and the Ure (essentially the same river), which is navigable from the sea up to Ripon. One of the clubs I belonged to had to take legal advice about non members fishing the club's stretch of the Ure from boats. The legal advice was that on this stretch of river, fishing rights belong to the riparian owners and their tenants and anglers fishing from boats are poaching unless they have consent from the riparian owners or tenants.
The rules for the Thames might be different.
I am a little late but this isn't quite correct. There is a legal right for anybody to fish
tidal water, including tidal rivers, from boat or bank. Except in very unusual circumstances (Royal Charter, special/local legislation ) this applies to all tidal rivers in England . But the right to fish from the bank is largely illusory , as there is no legal right of access above the high watermark - so when your club book gives you the right to fish on a tidal river , it is actually giving you the right of access , as you already have the right to fish the water.
There is no right to fish
navigable water from a boat - permission is required unless the water is also tidal .
In our friend's example , this means you can fish the Ouse as of right up to the locks at Naburn, below which it is tidal, sometimes spectacularly so... But above the tidal limit , you need a ticket, whether you fish from boat or bank - except for any explicitly free water
A lot of the legal stuff is actually pretty theoretical - if your club only owns one bank you only have the right to fish up to half way across but nobody takes this very seriously . There is some misleading folklore about wading - one common myth is that it's ok to wade , and fish, more than half way across even if you don't own the far side rights 'as long as you keep facing the far bank , and not facing your own' . Not so , but widely believed .
.