You're correct, HR is there to benefit the company. However, in this case, the goals align. OP wants to stop being sent objectionable material while at work. HR wants employees' actions to not open the company up for litigation. Being able to prove that dickhead is engaging textbook harassment while on the clock should be an open and shut case.

All of this is to be taken with a heaping handful of salt, since regulations differ wildly by jurisdiction, but this seems pretty clear cut to me.

This is exactly why HR departments exist. Had OP collected evidence, told management with a paper trail, and they failed to stop it? Or worse, told off OP because they don't want to deal with it?

The jerk could maybe get charged with a misdemeanor related to harassment or misuse of technology... Maybe the UK has something harsher or more specific, but at the end of the day it's a bit extreme to put someone in jail or pay OPs wages if they were forced out of work

The company on the other hand? They have a legal obligation to maintain a safe work environment. They also have deeper, easier to access pockets. A lot easier to get a lawyer to pursue that, which is expensive even if they win in the end

If they're clearly shown to have not taken reasonable action, they'd at least be on the hook for any lost wages or medical costs (not sure what decent therapy runs over there, less than the US I'm sure but I'm guessing not cheap). Even if OP quits or decides not to show up, it could be until they get a new job at similar pay with some extra thrown on top

HR's job is to cut this off before OP needs to be paid off, or much worse finds a lawyer. They don't care about the employees, so safest could be to fire the guy - the least they're going to do is officially reprimand the guy and follow up with OP to make sure it's not worsening and OP isn't feeling litigious

Which is exactly why not having an HR dept is only detrimental for the company, not the employee. If the company doesn't have an HR dept, they should consult a lawyer for a hostile work environment case. The lawyer will probably say he should first at least let his supervisor know, and if nothing is done, or if they retaliate, then they can show them why an HR dept is a good investment.

You're correct, the HR dept is there to protect the company. And the actions of the employee sending gore vids potentially harms the company. Thus, HR will protect the employee when it protects itself. Think how HR would step in if someone was sending porn. That would harm the company. HR would intervene.

They only don't do shit when they can get away with it. Anything that a court would find absolutely objectionable (not maybe) will be curtailed.