in the us
Fishes are excluded from most US laws that protect animals: many criminal state anti-cruelty laws, slaughter laws, transportation laws, and research and captive animal laws.
Criminal state anti-cruelty laws protect some animals from “unnecessary suffering.” They are mostly used to protect animals we keep as companions (so fishes who are kept as pets may be protected). Some of these laws don’t mention fishes at all (they are not even considered), and some exempt categories that fishes fall into (like animals who are farmed or used in research).
The federal Humane Methods of Slaughter Act requires that some animals be rendered insensible to pain before being slaughtered. The Act applies to farmed land animals besides birds (although birds make up the majority of land animals slaughtered for consumption), and does not apply to fishes.
The 28 Hour Law requires that farmed animals are only transported for 28 hours before they need to be unloaded for water, food, and rest. The law does not apply to fishes.
The Animal Welfare Act provides some protections to animals used in research, exhibited for entertainment, kept as pets, and during their transport in commerce. (The protections are not that certain animals cannot be used in these ways, but the standards of care animals should receive when being used for these purposes.) The law only applies to warm-blooded animals. Fishes are cold-blooded (except the opah), so it leaves the majority of animals exhibited in public aquariums unprotected.
Fishes used in research may have some regulatory protections. Any vertebrate animal used in research performed or sponsored by the US is covered by the Public Health Service Policy on Humane Care and Use of Laboratory Animals. Fishes are also discussed in the Guide for the Care and Use of Laboratory Animals, and in 2012, there was also a Special Topic Overview on Aquatic Environment, Housing, and Management.
Fishes part of an endangered or threatened species may have some legal protections in the US under the Endangered Species Act.
in the uk
Fishes have more protection in the UK than the US. Although they are not protected by the Welfare of Farmed Animals (England) Regulations 2007 or the Welfare of Animals at the Time of Killing (England) Regulations 2015, they are protected by the Animal Welfare Act 2006, which says that animals cannot suffer unnecessarily.
EU regulation 1099/2009 also protects fishes, but only as to the key principle, which is that “animals shall be spared any avoidable pain, distress or suffering during their killing and related operations.” (But after the UK leaves the European Union, this regulation may no longer apply.)
The UK has opinions from its Farm Animal Welfare Committee on the welfare of fishes on the farm and at the time of killing, but these standards are voluntary and do not have the force of law.
The Animals (Scientific Procedures) Act 1986, which protects animals used in experimentation from “avoidable suffering and unnecessary use,” also protects fishes.
Many laws in the US and the UK are limited to prohibiting “unnecessary” suffering. Courts defer to industry standards in determining what is “unnecessary” suffering, so if something is an industry-wide practice, it is deemed that the suffering caused by it is necessary.
Legislation to Protect the Welfare of Fish by Kelly Levenda in Animal Law Review Vol. 20 (2013).
How much suffering is necessary? The sad state of UK animal law by N. Cargill, Sentience Politics (2016).