The point is that even if the numbers in hospital are equal vaxxed/unvaxxed, that means you're at least 4x more likely to end up there if unvaxxed - or look at it another way, three quarters of the beds could be emptied if everyone was vaxxed.
Not specific to the status in London right now, but an interesting read and no doubt pins down some of the factors
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/952716/s0979-factors-influencing-vaccine-uptake-minority-ethnic-groups.pdf