The wk 4 report states:
The rate of hospitalisation within 28 days of a positive COVID-19 test increases with age, and is substantially greater in unvaccinated individuals compared to vaccinated individuals.
Defined as:
Cases presenting to emergency care (within 28 days of a positive test) resulting in overnight inpatient admission, by specimen date between week 52 2021 (w/e 02/01/22) and week 03 2022 (w/e 23/01/22)
The plot looks like this:

That looks like a pretty good argument that the vaccines prevent hospitalisation. But is it the whole story?
To investigate further, you'd need better data. Data on what these people were presenting with, their pathway through the healthcare system and outcome (as in, there's a big difference between an overnight stay for observation and ending up in ICU breathing through a machine). Such data does exist, in the form of EPRs (Electronic Patient Records), but are not publicly available (even anonymised).
Long story short, someone (who knows what they're doing) got hold of a large dataset of EPRs (about a quarter of a million, that ran up to last September) and analysed it.
What he discovered was that, while the data appears to show vaccine effectiveness against 'Covid-19' hospitalisation, it also appears to show that the 'Covid-19 vaccine' is effective against such things as severity of injury from playing sport, alcoholic intoxication and food poisoning, curing cancer, diabetes, heart failure, hang gliding, diving, horse riding and doing strange things with [your] private parts.
No wonder people are 'queuing up' to get them.