I'm a U.S. native speaker. I have NO TROUBLE AT ALL communicating with British speakers when we are talking to each other and faintly aware of being from different countries.
For years I worked at a company with offices in the U.S. and England and we'd have teleconferences and discuss all sorts of details with British colleagues and there was no language barrier.
I didn't always understand everything the Beatles said in their movie, "A Hard Day's Night," for example. I always understand Alec Guinness, even in British comedies like "The Lavender Hill Mob."
If I were to overhear young Brits speaking rapidly and colloquially to each other, using slang, yes, I'd could have trouble understanding. The same thing is true within the U.S. of regional accents and dialects, and across the generation gap. The first time I texted my 14-year-old granddaughter and she replied "k" I didn't know what she meant.
The most serious transatlantic understanding I've ever had occurred when I worked at a company that was in the middle of a mass layoff. A colleague I knew well, who was from Northern Ireland, came by my cubicle and said "I got the chop" (I've been fired, laid off, let go). I thought he said "I got the job," because "got the chop" isn't U.S. usage. (The U.S. equivalent would be "got the axe.") I didn't say "congratulations" or anything terrible like that, but there was a brief moment when I had to ask him to explain, and it was embarrassing to me.
Just for fun I took the Oxford Placement test here, and was surprised and humiliated to receive only a C1. It was due to the British/American language difference. In the spoken dialog I was aware of British turns of phrase and wasn't exactly sure what subtleties were being conveyed. In real life, this wouldn't be a problem because when a U.S. and British speaker are talking to each other, we would unconsciously simplify our speech just a bit.