There were originally two long barrows here together - as seems the case at a number of other Sussex sites.
The one at TQ363027 is on the crown of Beacon Hill. Although it is up to a metre and half high, it's been messed about with over the years - one particular indignity being the loss of 12m length from its north end "to improve a cricket ground" in 1863. A burial chamber and other interments were noticed at this time (presumably as they were lobbing the bones into the 19th century equivalent of a skip). Apparently the hill was used for a beacon fire on the approach of the Armada: so it's a site chosen for its prominence throughout the millennia.
The other long barrow is at TQ364025, but it's probably only visible as a mark in the grass - the flanking ditches were dug into the chalk beneath. You'll be pleased to hear that it's fallen prey to a 'sport' related injury too; this time in the name of miniature golf.
Kipling lived in nearby Rottingdean and apparently walked up to Beacon Hill on the occasion of Queen Victoria's diamond jubilee, to watch the bonfire being lit in response to the signal chain of beacons moving along the coast.*