Hi Charlie,
Hope this doesn't cause any confusion, I didn't go to Lulworth Cove after all, instead I went to Durleston Country Park, Near Swanage, the
Lulworth Skipper are usually later emerging there than at Lulworth Cove. I understand that the insect has now emerged at Lulworth Cove and I'm sure you will find them in reasonable numbers during your June visit, I saw them in good numbers at Lulworth Cove on a date roughly similar to yours in 2012.
Regards
Essex Skipper - I 'probably' saw them at Durleston on my visit last year, no photo to positively confirm though

Saw none at Lulworth Cove in 2012, it could have been a bit too early.
Good luck with your visit and keep checking the sightings page for the latest before your visit
Regards,
Bill
"When in doubt...venture out"