There are very few legal restrictions on the fish that the UK spearo may catch. It is illegal to spear salmon, trout ,shellfish or freshwater fish, and there are legal minimum sizes for most fish (link) , but that is about it.

The really slow colourfull fish are called Wrasse, and there are a lot of them. Shooting these is far to easy and unfair, they also taste crap ( the french eat them, need I say more).

There may be few legal restrictions, but most spearos fish with conservation in mind. Only shoot fish you intend to eat.
By far the most sought after fish in the UK is the Bass. Many experienced divers hunt bass to the exclusion of all else. It is unmistakable, with its silver colouring and large mouth. Bass tend to be quite wary, and it often takes beginners some time before they spear their first bass. Small fish up to 2-3lb are often in large schools, larger bass are normally on their own or in pairs (occasionally big bass school up, an amazing sight!) Agachon is the most common technique, but big bass can also be found in holes, or resting under the kelp. Bass are excellent eating.

Mullet are often seen in stringweed beds or along rocky shores, and are easily identified by their silvery bodies with horizontal black lines. Clean water mullet are quite good eating, but those from harbours can be a bit muddy tasting.

Pollack up to about 1lb weight are found everywhere, and are often the first fish a beginner spears. Bigger pollack are normally in deeper water. Pollack are not bad eating (they make good fishcakes), but do go off very quickly. Ideally they should be gutted before leaving the water.

Flatfish are normally found on a sand or mud bottom. They are all good to eat, but some are better than others. The trick with catching flats is to spot them when they are buried in the sand, sometimes all you see is the edge of a fin, or an eye, or even just a change in the pattern of sand ripples