It's a strange name, isn't it? Awkward Hill is a very steep hill, rising abruptly from the River Coln. You can quite see why it's called "Awkward" - it's a sort of blip or bump right in the middle of Bibury.
If you go down the other side, the lane is called Hawkers Hill, as in hawker, or pedlar. I keep meaning to look into this, to discover whether Hawkers Hill is a corruption of Awkward Hill, or whether Awkward Hill is a corruption of Hawkers Hill.
If anyone knows where the name comes from, I'd love to hear from you. When I decided to move to Bibury, my family thought the name was hilarious. It was even suggested that I use the blogging name Awkward Cow. But I think not.