At one point I lived with my mum in a village just off it, and my dad lived in another village off it about 9 miles away. I walked that route often, alone and with a friend, in all seasons, sometimes through the night.
You definitely have a sense of it being ancient, and it's easy to imagine the people who walked it before you.
Be warned, in winter it can be very challenging to cycle along. It becomes deeply rutted due to off-roaders, and your pedals will strike the side of the deep, water-filled ruts. I cycled the whole thing (in sections) with a friend one winter. Hard work, and fell off many times.
Checkout the White Horse and nearby ancient monuments, too https://en.wikipedia.org/wiki/Uffington_White_Horse