The so-called Mystery Towers 
were built towards the end of the First World War (1914 - 18) at the entrance to Shoreham Harbour, Sussex.

They were intended to form part of a line of 12 towers that would have been sunk onto the Varne Shoal in the Straits of Dover between Dungeness and Cap Gris Nez. Linking them were to be steel boom nets to block the path for German U boats on the towers would be equipment for detecting U boats trying to run the gauntlet. Guns on the towers and surrounding minefields were intended to protect them. 
Shoreham had a suitable calm water area - The Gut and supplies of sand and shingle, so in June1918 construction began on a number of the towers.

They became known as 'The Mystery Towers' as a result of the usual secrecy surrounding such a project in war time. It is reported that over 3,000 civilians and/or 5,000 army personnel were working on them at times. Two of the planned towers were almost complete with three more half constructed when the November 1918 Armistice came. After the war was over, two were finally completed to allow for research. 

 Rising 180 feet from an approx. 190ft base, 9,000 tons of concrete formed a honeycomb in a hexagonal shape rising in narrowing stages. On top of this was a 1,000 ton, 100ft steel cylinder for 90+ men, supplies and submarine detection equipment, for which there was a special electricity generating facility. 

A railway link was laid from the dock line under the road to the western arm of Shoreham Harbour, this then ran along the bottom of the embankment, across Kingston Lane, swinging across the coast road and along the edge of the wharf, it crossed the single lock that was there then, on a movable contraption, then jointed several miles of sidings serving the works. This line is just visible in the picture below.
The route of the  line is clear in the vertical picture, though this one appears to have been taken after the rails and sleepers were lifted

After the war ended, there was much fuss over what was to become of the redundant structures and eventually on 12th September 1920 one of the towers was floated off to form what is now the Nab Tower on the Nab Sandbank off the Isle of Wight, replacing the former lightship. It serves as a navigation station for the busy shipping lanes. Since 1983 it has been fully automatic, conversion is said to have cost some £200,000, in comparison to the original reputed cost of some £1,000,000 each. 

The other completed tower was demolished, no use being found for it in peacetime, It is reported that it was a good thing it was not actually needed as it was 6 feet too wide to leave the harbour mouth. The broken up concrete was used as foundations in many local buildings, including greenhouses in Worthing.

Two Towers are at the left of photo, most of the fields visible are now built on.
Visible on the right are the huts on Southwick Green for the workers.
In the centre bottom, is 'The Gut' which is now reclaimed and used for harbour wharfage.
The new gas power station would be below the 'wick' of Southwick.