It's the Johns Hopkins University CSSE dataset, and recovered cases are indeed not properly tracked for some countries. But you can just look at the crude numbers of confirmed cases and fatalities to see that the situation in Germany and the UK follow different dynamics (cf this plot[1] of the new confirmed cases, though the difference is of course in part due to the testing rates),
However, from looking at the daily fatality rates, you're right that the UK might indeed be already past the peak as well.
"This file contains information on the deaths of patients who have died in hospitals in England and have tested positive for Covid-19. All deaths were reported during the period specified below and are recorded against the date of death rather than the day the deaths were announced."
It doesn't include people dying in nursing homes. It doesn't include people dying in care homes. It doesn't include people dying in supported or sheltered accommodation. It doesn't include people dying in prisons. It doesn't include people dying in their own homes.
From research we think care home deaths are a significant fraction of the total (between 30% to 50%), although we need more information.
We stopped transferring people from care homes to hospitals. We put them on palliative pathways instead of transferring them to ICUs.
https://news.sky.com/story/coronavirus-disappearing-so-fast-...
As for deaths, they have peaked in early April in England (see first spreadhseet "COVID 19 total announced deaths"):
https://www.england.nhs.uk/statistics/statistical-work-areas...