The NHM is free to enter, some special exhibitions charge for entry and I think some require free booking to manage crowds. There is a very strong encouragement to make a donation though.

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.

I find that less annoying than what some museums around Europe charge to let you through the door.

At least they're honest about it. (Though the suggested donations at "free" museums are usually pretty reasonable.) I'm not sure big city museums in the US are especially cheap either.

> I find that less annoying than what some museums around Europe charge to let you through the door.

I really don't get what you find wrong about this.

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.