One reason why the UK, Ireland, Iceland, and Denmark, have been bickering for years over territorial rights is that Rockall sits on the Rockall Bank, a massive sea bank which geologists believe may contain significant amounts of natural gas and oil. Added to this are the lucrative fishing grounds surrounding the island. All this makes Rockall a highly coveted prize.
The British originally claimed ownership on Rockall in 1955, when their 'annexation' forces invaded as a territorial claim. This prompted a fierce diplomatic fight where the status of Rockall as an island was put into question. John Ridgeway and Tom McLean during the 1980s perched themselves at the very summit of Rockall and remained there for one month in order to protest and validate Rockall's right to be an island.
- for further details see http://www.bbc.co.uk/dna/h2g2/alabaster/A755787