There are two or three long barrows recorded for this area. I was looking for the one mentioned in “Hampshire Treasures” at location SU479362 but there is no record of it on Magic or the OS maps.
It would have been at a place called “Bayley’s Clump” about 1km to the East. When I looked into this small copse the nettles and undergrowth was chest high so a winter visit is on the cards.
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I've now managed to track the others down and am adding them as sites. This one was called South Wonston West by the Royal Commission on Historic Monuments. South Wonston East isn't as far away as Bayley's Clump and is quite easy to spot from the road once you've found it! I'm afraid the good old Hants Treasures got the grid ref wrong...