This was the only example of this particular sea plant that I found on the beach between Boscombe and Bournemouth Peirs.
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I regret not finding this before now - five years too late then!
Anyway I agree, not with Sea Oak (you'll understand why if you search for Sea Oak in Google or iSpot) but with Halidrys siliquosa.
If you come Robert, please add the Tag MarineA1, via Edit. It will go straight into the Seaweed Project, though it might be the earliest post!
Lat/Lng: 50.71762, -1.86136
OS grid ref: SZ098908