I call this cape Danger Corner. The concrete platform comes to an end (facing northward). A large notice warns of slippery surfaces, recent rockfalls, quicksands, the tide. Steps descend to the left (this bit of coast actually faces north, parallel to Long Entry the coast is tucked in, or, to put it another way, Danger Point is a peninsula).
The beach that starts here is called by locals Back Beach, though the name is not on maps. It's the incurved end of the bay that stretches around to Charmouth. The first part of the overlooking cliff is Church Cliff, since the church (out of sight from here) is not far back from its top. Indeed the cliff is eroding dangerously back toward the church, as you can see by the massive wall intended to shore it up and the recent rockfall that has come down over the wall.
As the cliff curves onward and grows higher, it is called East Cliff.
If the tide is low (and preferably if you are wearing Wellington boots) you can venture out onto the platform of dark wrinkled rocks called Broad Ledge.
Or: walk the mile and a half along the beach to Charmouth.
Do this only if the tide won't come in while you are on the way! Have you consulted your little book of Tide Tables, which you can get from one of the bookshops in Broad Street? Best to take the beach walk when the tide is falling say, an hour or so after high tide. Not only will you have the longest safe time, but there is the most chance of finding fossils. They will have been washed out of the fallen rocks, and not yet found by other fossil-hunters.