There appears to be no articles or photographs in the local newspapers covering the building or an opening ceremony of the Skegness Clock Tower Island, so a little detective work was needed to pin the event down. From the related articles I managed to find, the event happened in Spring/Summer of 1959. (See below for the stories.)
The photograph below shows the construction of the Island in progress.
The first reference I found to the Clock Tower Island was in the Skegness Standard dated 7th January 1959, which announced that work was due to commence shortly:
This photograph appeared at Whitsuntide, 1959, but it doesn’t look as if work had been started on the Clock Tower Island…
Then, without further reference Hey Presto…the Clock Tower Island is now complete! The photo below formed part of a story published on 12th August, 1959, covering the Diamond Anniversary of a Diamond Anniversary monument. Other than the Mayor of Skegness ascending the stairs inside the Clock Tower to perform a ceremonial winding of the clock, there seem to have been no pomp and ceremony for the 60th anniversary of the Clock Tower, nor the completion of the new surrounding island. I really thought the Council would have buried a time capsule to mark the occasion. But maybe it did…see my post entitled Clock Tower Mystery Find
This photo printed in the 14th October, 1959 issue of the Skegness Standard shows the Clock Tower Island completed.