Here the evidence, (quietly) provided by the British government.
From p. 10:
The resurgence in both hospitalisations and deaths is dominated by those that have received two doses of the vaccine, comprising around 60% and 70% of the wave respectively. This can be attributed to the high levels of uptake in the most at-risk age groups, such that immunisation failures account for more serious illness than unvaccinated individuals. This is discussed further in paragraphs 55 and 56.