I haven’t heard of Lulworth Cove. But I take it you’re looking for more than just a nice green space with a nice views, like Primrose Hill or, as Queen Elizabeth Park (Formerly the Olympic Park). You might struggle to find something like Beachy Head or Cheddar Gorge within half an hour of London, but for a nice walk and BBQ, most of the above are perfect. You might also like Richmond Park, Epping Forest, or even Kew Gardens if you’re flexible. If you travel further there may be better options.
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