For instance 79% of the people >18yo who tested positive in December were vaccinated. And that's pretty much the % of people over 18 that are vaccinated in the UK. You get pretty much the same result for each age tranche:

                 Positive   of which     % pos test  % population
   Age            Tests      vaxed      vaccinated   vaccinated
   <18           395,335     57,284        14%        35%
   18-29         257,526    181,705        71%        60%
   30-39         254,435    193,623        76%        65%
   40-49         230,670    195,908        85%        77%
   50-59         147,033    129,440        88%        85%
   60-69          58,233     51,037        88%        90%
   70-79          18,858     16,263        86%        95%
   >80             9,067      7,658        84%        95%
   Total > 18    975,822    775,634        79%         

p36: https://assets.publishing.service.gov.uk/government/uploads/...

You had the same outcome in November, i.e. pre-Omicron.

Ah, yes. That's not a very useful stat compared to something like case-rate-per-100K since the denominator could be all over the map.

What's the case rate per 100K at the population level there?

Edit: actually, didn't find exactly that table, but did find a section in the doc you link, https://assets.publishing.service.gov.uk/government/uploads/..., on page 14, that shows vaccine effectiveness remains against symptomatic disease as a result of a study against delta and omicron both. But I would love to see the overall case rate to know about asymptomatic disease too.

Not sure what you mean by denominator? The denominator for vaxed positive cases is all positive cases. The denominator for vaxed in the population is total population (within the age range).

The % per 100k is available p40 of the same pdf. But I find that much harder to read given that the size of the vaxxed and unvaxxed populations vastly differ.

In "percent vaxxed among positive tests" you're only looking at those who got tested and were positive at a snapshot in time. At the very least, you also need to include all the people who tested negative. You complain that the size of the vaxxed and unvaxxed populations are vastly different but then use numbers where you look at just positive tests, ignoring counts or negative counts. That gives you numbers with even more potential sources for skew!

The table on page 40 is consistent with US data, where case rates at the population. It says to read in conjunction with pages 32 to 34, which basically says "stats won't be as accurate as formal assessment of vaccine effectiveness, please see the formal data." The formal data suggests effectiveness against transmission. The raw cases-per-100k numbers agree. Yet you latch onto a different number - another one that the report says isn't authoritative for those purposes either - to claim the data shows ineffectiveness! That seems backward.

The UK is considerably more vaxxed and boosted, enough that the dynamics could be different.