The material shown in the example is of two clearly distinct classes: on the one hand, there's sexual material, and on the other, there's any other shocking material of animal cruelty. So let's treat those separately, using the denominators of OP.
materials showing sexual abuse of animals
Mere possession of such material could be prosecuted as "Extreme Pornography", and showing it in public is not just possession but atop that public display of such material:
Possession of extreme pornographic images is an either way offence. The maximum penalty for possession of extreme pornographic images involving necrophilia or bestiality is two years' imprisonment and/or a fine; for other images it is three years' imprisonment and/or a fine.
An offender aged 18 or over and sentenced to two years' imprisonment or more is liable to notification requirements pursuant to section 80 and Paragraph 35A Schedule 3 Sexual Offences Act 2003.
The public display could also trigger Outraging Public Decency, in case the prosecutor can't find a better match somewhere else:
Outraging public decency
It is an offence at common law to do in public any act of a lewd, obscene, or disgusting nature that outrages public decency. This offence should only be considered if the incident falls outside the statutory offences, for example if it is not possible to prove the mental element required for an exposure offence or exceptionally, if the offence merits a higher penalty than that available in relation to the statutory offence.
gruesome cruelty to animals, gory slaughter of animals, sadistic beating of animals
If the material would be shown just online, it would be a breach of the Online Safety Bill 2022, and would need to be deleted by an online platform:
Including Animal Cruelty Content within the Bill
- Placing obligations on service providers to remove animal cruelty content not only falls within the spirit of the current Bill, but possibly within the scope. The scope of the Bill is to place duties on service providers to remove illegal and harmful content, placing particular emphasis on the exposure children have to both of these. Animal cruelty content is both a depiction of illegality and causes significant harm to children and adults.
The acts depicted in the video might constitute a breach of the Animal Welfare Act 2006, and would be prosecuted separately. Note that the very law also illegalizes any Videos of Animal Fights but for narrow exceptions. In general, those are illegal to possess, supply, and show under Section 8, (3) (a)-(d). Assuming no Animal Fights inside the UK are depicted, and the person showing the material was not part of producing the video, then this law does not apply obviously.
The act of showing the material on the street might be Intentionally or recklessly causing public nuisance under Police, Crime, Sentencing and Courts Act 2022, Section 78:
A person commits an offence if—
(i)does an act,
(b)the person’s act or omission—
(i)creates a risk of, or causes, serious harm to the public or a section of the public, or
(ii)obstructs the public or a section of the public in the exercise or enjoyment of a right that may be exercised or enjoyed by the public at large, and
(c)the person intends that their act or omission will have a consequence mentioned in paragraph (b) or is reckless as to whether it will have such a consequence.
The person showing the material:
- shows material, which is an act (a),
- the material shown obstructs a part of the public in their
- enjoyment of the right to eating what they want, including meat, (b ii)
- exercising their right to just walk with their kids unmolested by shocking immagery (b ii)
- which is in part the intended purpose of the show. (c)
There also is the 78(b)(i) variant, where you need to keep in mind that "serious harm" has a definition:
(2)In subsection (1)(b)(i) “serious harm” means—
(a)death, personal injury or disease,
(b)loss of, or damage to, property, or
(c)serious distress, serious annoyance, serious inconvenience or serious loss of amenity.
As such, the definition of 78(2)(c) would be triggered - the imagry is a serious annoyance or serious inconvenience or loss of amenity to the people wanting to eat meat or just go into town with their kids without seeing such gruesome material.
It would require a "reasonable excuse" for the act to be excusable under subsection (3). If informing the public of the meat industry handling is such a reason is up to the courts to decide.