As a tangent, I find it a bit annoying that so many UK museums advertise free pretty aggressively and then provide such "very strong encouragement" as you put it to attend. Mind you, there's less direct pressure than there is in some places. The Met in NYC used to have an optional but not really optional policy for museum admission as you got your pin though it now not optional at all for non-NYC residents.

Free to enter since 2001. Which means now they have (more) donation boxes.

My local museum started charging for entry a few years ago, along with a refurbishment, new exhibits, a bigger gift shop and a push to attract more tourists. So now it's horrible. I'm not sure what the unifying mistake is in both models, free entry and ticketed. I think the error might be in trying to serve the public.