"This claim has been shot down by Public Health England and most fact checkers."
Your statement is false
https://www.br.de/nachrichten/wissen/delta-variant-not-more-dangerous-for-vaccinated-people,Sg5VJIM"A total of 123,620 Delta cases were detected during this period. 10,834 of those infected had already received two doses of vaccine, while 71,932 were unvaccinated. Of the double-vaccinated, 118 had died, compared to 92 of the unvaccinated"
This article, which tries to prove your point fails miserably. The double vaccinated deaths are far more with fewer cases. It argues age and health are the biggest factor. Well duh, of course age and health are the biggest factor. At least the vaccinated rate of infection was lower. As Israel and Gibraltar show, high vaccination rates don't stop the virus or death. However, natural immunity works 13 times better than the virus and yet it gets completely ignored, just as the President ignored it yesterday.