There is an island just off the coast where we live, The Island has a sand bank which connects it to the main land. assuming that the distance is less than a Tchum would one be allowed to walk to the Island on Shabbat?

Based on the information you have given me, you would be allowed to walk there on Shabbat. Be aware that the tchum Shabbat is (2000 ammot) 960 meters from where the settled area of the mainland ends.