I believe UK ages 25-34 average height is around 177.8 cm (you can check it on wiki). Height is still increasing but not very much. The BBC says the class distinction in height levelled off with the generation born in the early 1960s or 70s (forget which now) and now we are likely getting very close to the peak. "Anglo-Saxons" are Caucasian, sure, but genetically more Celtic than Germanic by and large (I think it's about 60/40) which makes them a little shorter than their purely Germanic cousins, perhaps. I guess those of pure southeastern English stock are probably closer to 5'11 on average though. I think Welsh guys (25-34) are about 5'9.5 on average, which makes sense as Wales is still the poorest country in western Europe or something.
It's true the 95th percentile in height has gotten higher and higher, though. But the 50th and 75th percentiles seem to be about the same. Although the lower percentiles might also have risen. I think 5'8 (my height) for all sections of the population is in about the 33rd percentile, but for my generation it is in the 25th or so! That could be just because old people shrink an inch or two though.
I'm not exactly sure how it all works, but I wouldn't actually want to be above the 95th percentile anyway. Above the 75th would be really nice (which is incidentally perhaps a few mm lower than 6 ft) but 5'10 is fine guys. Stop worrying. Most girls really can't tell that well, because most girls are shorter than 5'6 (I think 5'4.5 is average for 25-34 year old white women in the UK now). I went through a massively self-confident phase when I was a bit younger and girls used to ask if my height was 5'10 (I was probably not even quite 5'8 then). Now one of the same girls recently asked me if I was 5'6! That's just because I've been down for a few years and am much more introverted.
5'10 with confidence (and maybe some subtle lifts) is as good as an averagely confident 6 ft anyway, imo. And 6 ft is basically as good as 6'2. Unless the lady in question is VERY particular/unusually tall and cared a lot about height. I guess in the corporate world things might be different but that's not my kind of place anyway. Also, depends on where you live, what the culture around you is and so on.
Er, anyway, you're welcome for the essay.