Don't overlook that a navigation may be subject to local byelaws and controlled by the port authority, or British Waterways. A right to navigate is not quite the same as a right to access, and is not necessarily free.
For paddling to the coast from the barrage, I would suggest that there is almost certainly a requirement to contact some administrative body, perhaps a port authority, perhaps estuary control. It might not be the busiest estuary around Britain, but you do stand a fair chance of meeting with big ships. It may simply be that you are supposed to contact them to get information on shipping movements and advise them what yours will be so they can make sure traffic is kept apart, there may be no legal background to it. I don't know about the Tees particularly.
The Clyde for many years was thought to be out of bounds due to shipping etc. but it seems this was mainly an impression put about by overzealous lifeguards and the fact that all the access points are locked. Since the land reform things have been cleared up a little and it is now possible to launch in Glasgow and paddle to the sea, there are certain requirements though and some of my own tips:
- You need to contact SCA for instructions and code for a gate to get to the river at Glasgow Green
- You must launch below and not shoot the barrage (it is walled in death anyway)
- You must contact Clydeport Estuary control, preferably by VHF to find out about shipping movements (if using VHF you can receive updates)
- If you are instructed by estuary control to pass a certain part of the river on a certain side due to ship movement, please do so.
- There is alternative access at the transport museum at the Kelvin confluence, I beleive access is free but the car park isn't. I know the chairman of the maritime trust is keen for people to use the slipway and I did advise him that I didn't beleive people would be prepared to pay. I have since heard rumour that the arrangment is not the easiest to use by kayak, which is kind of a shame because before the museum was built the remains of Inglis shipyard slipways were there and they were perfectly useable by kayak, I egressed from the Kelvin on them a couple of times :-)
- Don't forget the seaplane uses the river in the city centre, it has to make a pass before landing to check for obstructions - kayaks are not that visible though.
Basically it is physically impossible to access or egress the river for much of the distance down to the coast, but it is permitted.
Once you get down the estuary, depending on your destination you might stray into an area classed as a Naval Dockyard, there are certain rules in those which should be followed and it will be useful to have VHF.
Most of the time kayaks can paddle completely anonymously in these sorts of places without ever being in or causing any danger, but one can understand why the authorities prefer to know we are about.