> The British pronounce it as "istory," so they use "an" before.

"The British" aren't monolithic and neither are our approaches to this.

I certainly don't say "it is an historic day" or "staying at an hotel" with the soft H, because to me, in the 21st century, it's an upper class affectation (I am from a middle class background and from the commuter belt 30 miles south of London).

I moved to a slightly posher place and I know people who do say "an historic day" (soft H) still but it's largely out of habit/age/schooling.

The BBC have stopped doing this, as a rule. The monarchy have moderated this aspect of their speech too — I am sure I remember the younger Prince Charles say "an historic day" with the soft H, but I am fairly sure he would now say "a historic day" with the hard H; he has been trying to progressively moderate his RP accent for the last 25 years or so.

ETA: clarification in reply to reply

The majority of British accents would pronounce the 'h'.

I have seen an American book, published in the 1960s, whose title included "An Historical Survey".

For me, on this one, if there's an "an", it pushes me to not pronounce the "h" in the next word, even though I consider it silly to pronounce "historical" that way.

I don't think so. This one seems to defy the rule.

"A his-toric day"

"An his-toric day"

Both seem to work correctly with American pronunciation.

Journalists and films seem to use "an historic" with an American accent, which breaks the rule but still feels correct.

For most words the indefinite article is clear. This one feels weird.