Interesting. But there's a couple of features in there that make me leery of relying on this.
First, the table there is tracking convictions at jury. Clearance rates, especially for property crime, have never to my knowledge been high; if we assume similar figures they'd be undercounting reported crimes (most comparable to the crime statistics we're familiar with) by a factor of three to five, and undercount committed crimes by more. That isn't necessarily a good assumption, though, and there's the rub: we can't use conviction rates to estimate crime rates unless we know something about how likely cases were to make it through the system.
Second, buried in the bottom of that page there's a sentence saying that about 17,000 summary convictions (excluding some minor fines) were imposed independently by police magistrates. No information on type, which means the table would further undercount crimes by some unknown proportion depending on how likely summary punishment was. But 17,000 is roughly four times the total jury convictions cited, so it'd probably be large.
I haven't been able to find another source going back to the 1830s yet, but this data suggests that as many murders were recorded in London in the late Victorian era as in the mid-Sixties, when population was about 20% higher. (Population in 1838 was much lower -- the city grew hugely over the 19th century.)
Well, I don't have an intimate relationship with this data, this was only a Google quickie :-D But I think NRx made a big deal out of the safety (as they claimed) of Victorian London and it's something they bring up regularly. It might have started with Mencius Moldbug, but I'm too lazy to go looking for the original write-up which, IIRC, included some data analysis.
There's a new paper arguing, contra Pinker, that the world is not getting more peaceful:
On the tail risk of violent conflict and its underestimation
Pasquale Cirillo and Nassim Nicholas Taleb
Every claim in the abstract is supported by the data - with the exception of the last claim. Which is the important one, as it's the only one really contradicting the "long peace" thesis.
Most of the paper is an analysis of trends in peace and war that establish that what we see throughout conflict history is consistent with a memoryless powerlaw process whose mean we underestimate from the sample. That is useful and interesting.
However, the paper does not compare the hypothesis that the world is getting peaceful with the alternative hypothesis that it's business as usual. Note that it's not cherry-picking to suggest that the world might be getting more peaceful since 1945 (or 1953). We've had the development of nuclear weapons, the creation of the UN, and the complete end of direct great power wars (a rather unprecedented development). It would be good to test this hypothesis; unfortunately this paper, while informative, does not do so.
The only part of the analysis that could be applied here is the claim that:
This could mean that the peace since the second world war is not unusual, but could be quite typical. But this ignores the "per capita" aspect of violence: the more people, the more deadly events we expect at same per capita violence. Since the current population is so much larger than it's ever been, the average time delay is certainly lower that 101.58 years. They do have a per capita average time delay - table III. Though this seems to predict events with 10 million casualties (per 7.2 billion people) every 37 years or so. That's 3.3 million casualties just after WW2, rising to 10 million today. This has never happened so far (unless one accepts the highest death toll estimate of the Korean war; as usual, it is unclear whether 1945 or 1953 was the real transition).
This does not prove that the "long peace" is right, but at least shows the paper has failed to prove it wrong.