The "trackway" you saw is probably the snaking earthwork that marks the boundary of a Bronze Age field system on Stockbridge Down. It is mysteriously marked as 'earthwork' on the pink OS map, but it does have its own page here on the portal. I always think its amazing that such small-scale earthworks have survived the ages: most of these must have been erased by ploughing over the centuries.
There are a many spectacular medieval trackways in the Hamphsire chalkland - they are sometimes called 'hollow ways' because of the way that over many centuries the traffic resulted in deep grooves in the chalk. The chalk from the 'ditches' of the hollow ways was eroded away, in contrast to the chalk from the prehistoric earthworks which was deliberately dug and piled up to form banks.
Some trackways, like those approaching Winchester from the South Downs, have prehistoric origins, although the actual hollow ways we see today are certainly a result of the heavy medieval traffic.
Note that we (modern society) have added our own "hollow way" through Twyford Down in the form of the M3 cutting, which truncates the ancient route.
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