Lubo,
All 'navigable' rivers and canals, i.e. Those that can carry powered vessels', are controlled by an authority tha have the power to grant navigation.
Although a kayak is not powered it still needs a permit.
The Angling Trust can offer a permit but it only covers those controlled by the Canals and Rivers Trust. The BCU permit adds the waters of East Anglia, controlled by the Environment Agency, plus the Norfolk Broads and The Thames. Pricing is similar.
Non-navigable waters are much more difficult. There is a legal debate running as to whether there is an ancient right of navigation on all rivers (BCU) or whether the rights are held by the owners of the land that borders the rivers (AT). There is no definitive ruling on this YET!
You can approach fishing clubs or landowners for consent. The Paddle Points site points out areas that are OK generally.
So you need a Navigation permit, a fishing permit and of course a rod license. I should add that if you are paddling a stretch for which you do not have fishing rights and you have tackle with you then you technically commit an offence under The Theft Act 1968. I always carry all the permits with me along with some cash so that if I accidentally enter a stretch wrongly I would very politely off to pay a for a ticket. Anyone asking for such payment must have identification! If asked to leave then do so politely.
Sorry that it is all so complicated but as the owner of this site I have to give the most accurate information that I can.
I hope this help clear things.
Terry