Observing animal behavior underwater presents several challenges not faced by those in the terrestrial world. For bird-watchers, all you really need is patience and a good set of binoculars. Any decent sized sea cliff in the UK will attract a horde of twitchers, cameras and lenses at the ready, who can blissfully watch birds taking off, landing, feeding their chicks, and arguing over nesting spots. Similarly, back-garden bird watchers may have to contend with shyer species more likely to take off when noticed, but a diversity of feeders and nest sites (and an absence of cats) can reliably guarantee that some bird behavior will be seen.
Underwater, the biggest challenge is time... depending upon your equipment and depth you may have anything between ten minutes and two hours to observe as much as you can. Finding fish or other sea life that are doing anything interesting (e.g., not simply swimming or resting) becomes a race against time with your air supply the limiting factor. Diving a wreck, or a site known for a given species can up the odds significantly, but for some of the more interesting animals, it all comes down to luck.
Unless you are using a rebreather, you are also noisy as hell under water and likely to disturb or scare off the animals you are trying to observe. Take a look at the octopus and the seal in the prior two videos... both animals are well aware of me, and neither is particularly happy that I'm around. The octopus is fleeing from me and sees me as a predator. The seal is taking a more wait-and-see attitude, but is clearly not comfortable being cornered by two divers. There is no sound on either video, but if I had left the sound in, you would hear the very loud sound of my breathing and exhaling through my respirator. Rebreather divers have an advantage here, as they are virtually soundless, and they are the equipment of choice for professional underwater photographers for this reason... ...but with a cost of roughly £5,000 for the kit and training, this presents a substanial barrier to entry.
Finally, its gets dark underwater, particularly in the UK, and its easy to miss a lot of what is going on around you. The seal and octopus videos were taken off the NE coast of England at around 10 meters... visibility is still good. This below is more typical:
Note how much darker everything is outside of the beam of the torch... (also the noise I'm making!) That means that a school of fish can be 10 meters away from you, just at the edge of your visibility, and deliberately avoiding this noisy invader of the deep! Quite a few times I have seen interesting shadows swimming at the edge of my vision, or just glimpsed something disappearing into a crevice, meters away from me but too far to see clearly in the murk.