Sea oak (Halidrys siliquosa) is common around the coast of the British Isles, usually covered by sea water and only seen at very low spring tides. However, remnants do wash up on the beach and can be from along the strand line from time to time, just like this piece.
Sea oak grows in big bushy structures up to a metre in length and is made up of constantly alternately branch strands. It is not as 'fleshy' as many seaweeds but it does have lance shaped bladders at the tips of each frond to aid buoyancy in the water. The speed of growth and the size it grows to is generally governed by the amount of sunlight it gets.
Extracts of this sea weed are used in skin conditioners and it is semi-cultivated for this purposeHalidrys siliquosa: the sea oak