There a byelaws to adhere to; where I am, I can take fish (with limitations) and as someone whom eats fish, I do - trout mainly. If we all took fish for the table though.. there wouldn't be any fish left I don't think.
The only fish really suited to a aquarium in the uk imo are 3 spined stickle back, (Gasterosteus aculeatus), and they need space. a group really should be in a 6ft plus tank, and even then, i would recommend only one male. Smaller tanks are okay just to observer breeding behaviour but never to house long term. A lot die in those tanks in science departments in schools.
Bulheads, or miller thumbs need highly oxygenated water, and if you ever do catch one it will be from very turbulent/fast flowly rocky water. I thought they were protected, but they are not. They don't grow massive, and they might do well in an aquairum, but it's the kind of fish that is best left in the river (I guess we could say that about all fish).
Minnows (Phoxinus phoxinus) do survive, but highly susceptible to stress - needs a very mature tank, high numbers (so again, a big aquarium) and always treat them for parasites.
If you can get a young one, a Perch will do very well for a long time, but they get big and as one of my favourite course fish, I'd rather you left it in the river. That said, a Ruffe (Gymnocephalus cernua) would do fine I think. I have caught them in all sorts of water, and they're an invasive species in US.
If you're wanting a loach, only the Stone Loach isn't a protected species; you can get these from some lfs.
You do not need a fishing licence to fish with a small net (you know butterfly nets kids use), but there are obvious things, i.e don't start using throwing nets. You will be fined, heavily.