One of the best big-view, big-history walks on this list — hillfort, ancient white horse and a genuinely striking monument all in one outing, with a free car park right off the A4. Steep in places, so it's a proper leg-stretch rather than a stroll.
A big National Trust downland estate above Cherhill and Calstone Wellington, taking in the Cherhill White Horse (cut into the chalk in 1780 and also known as the Oldbury White Horse), the Iron Age earthworks of Oldbury Castle hillfort on the summit, and the 120-foot Lansdowne Monument obelisk designed by the architect of the Houses of Parliament. You can't walk on the horse itself, but the down and hillfort around it are open access.
National Trust land — usually free to walk; some sites charge for parking.