As I understand it, the boundary between the sea and a river is the 'Normal Tidal Limit', (NTL). This is often marked on 1:25000 OS maps. These maps are viewable by using bing maps and selecting the 'OS' display mode. For example, the Leven at Renton, as mentioned above, is shown here:
View attachment 64506
See the Wikipedia article 'Head of Tide'. Also the info on marine licensing at
https://www.gov.uk/guidance/marine-licensing-definitions
I can't see anything specific on the EA web site. A good idea to check with local tackle shops (if there are any) or local clubs.