I booked an appointment, took it in, told them what happened, and paid for a replacement. I was the second person that day he had dealt with for a screen replacement on a 6 - it's cheaper to replace the iPhone 6 screen than the 5/5S/5C/6+ for some reason.
Anyway, it took 15 mins and I now have a brand new undamaged phone. It cost £85 and I can claim some of that back on my credit card protection plan. I'd rather be honest - karma just kicks my ass if I lie, and the screen is white and not yellow at least.
I've only damaged one iOS device before, and that was an iPhone 4. That was stood on the floor, leaning vertically against the wall to charge from a wall socket, and it fell forward, so a drop of about 6 inches for the top of the phone, almost nothing for the bottom, and that still cracked the screen, so I guess it can be bad luck as much as how hard it's hit.
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Mine slipped from my pocket while seated at my desk this afternoon and dropped about 20"
This is the result
View attachment 495595
Those thin curved sides are definitely the vulnerable part. :-(
If you're OK paying for a replacement, now is the best time as they don't have the spare parts or refurbished phones yet, so you will get a brand new phone.