(S/E) The start is the main car park next to the visitor centre at Lulworth Cove(Grid ref. SY 821800). This can be a very busy place during peak times and if you prefer a quiet walk then do avoid peak holiday periods. From the car park take the broad paved path heading uphill west wards towards the coast. All the height gained on this section will be lost as you descend to Durdle Door and as you have guessed will have to be climbed again to return to Lulworth Cove.
(1) Reaching the summit of the first hill you get the first good view of the Dorset Coast with its fine white cliffs. Stay on the main South west Coast Path to reach Durdle Door where you can descend to the beach to get a better view of the rock arch.
(2) To complete the walk return by the outward route to the car park continuing past the information centre to reach the shingle beach of Lulworth Cove. Almost completely circular the cove provides a sheltered haven for small boats and is a pleasant place to spend some time before returning to the start of the walk(S/E).