I believe this was one - if not the very last - of the final passages to be made by RMV Scillonian (II) to Scilly from Penzance, and all the more momentous for the fact that, seen on the right, is RMV Scillonian (II) having just met and passed the newly commissioned RMV Scillonian III on the left.
The following slide in my collection taken in the evening after a day trip to St Martin's, shows the Queen celebrating her Silver Jubilee from the balcony of Buckingham Palace, on our television in a boarding house at Pelistry, St Mary's. (If that should provide a clue to the precise date.)