Edit - thanks to @jdietrich below there are some stats on this link, which shows a correlation between events you'd expect to increase the rush of domestic abuse, such as the Covid lockdowns: https://github.com/alphagov/govuk-design-system/discussions/... I do wonder how they got those stats though.
Edit 2 - I'm so glad this got posted! I've been wondering about this for ages and it's really nice to get some evidence for its use. Reading through the comments has also solidified my thinking around "why don't people just close the browser window" - many people who use honour-based abuse services are very computer illiterate, don't have time to learn about incognito windows / (Ctrl | Command) + W, and can only snatch computer time here and there. Abusers can look back at the browser history, but if the choice is between being discovered on an honour-based abuse website or the chance that the abuser won't look at the history, the second is clearly superior.
Edit 3 - I really wonder about the three-press shift keyboard shortcut. Real lack of discoverability, and my worry would be that the lack of consistency across sites would lead to situations where people are on non-gov.uk websites and think that keyboard shortcut would work there too. Although I suppose the fact that the first shift press activates the button in some way does tie it to the presence of the button on screen.
Edit 4 - It doesn't seem to be in use on any relevant gov.uk pages. The pilot on the "check for legal aid" pages seems to have ended and it's not on the pages about domestic abuse.