The safety of fishing was the argument used to the government by the Angling Trust, and it was swiftly rebuffed, including an implied criticism that now is not the time to be looking for loopholes. The problem is that you may think you are not at risk or putting others at risk, but as my mother used to say - it is the thin end of the wedge. Other, less responsible, people see you enjoying yourself with your hobby and they immediately think they should be able to do the same. So you rapidly end up with, for example, skateboard parks full of youngsters, beauty spots crammed with walkers etc. and we are back to square one! A critical time will be this weekend when everyone is getting stir crazy and the weather is due to be better.Imo the question is simple: can you avoid contact to other people while fishing and on the way to the fishery.
I don't see why fishing alone in a wide space after using your car to get there is any kind of risk.
On the other hand I can also understand the authorities. Anglers might use a train to get to the fishery. Also some fisheries are more confined spaces that are crowded and promote contact between anglers. Day License selling is also an unnecessary contact that can promote infection (unless they sell licenses online which some do).
In short, if you drive into the mountains and fish with the next person being more than 100 feet away from you there is zero risk.
But if you use public transportation to get to a small crowded inner city fishery after buying a license in person you are creating a lot of risk