The "cajones" appear to be "caissons" and the "cajoneras" are used to build them. As far as I can tell, they are simply referred to as "floating docks" in English.

On the page of FCC, the maker of the cajonera "Mar de Enol", they are called "floating docks," although this would seem to be rather poor attempt at a translation from the Spanish:

Through its Machinery Department, FCC has been maintaining a continuous investment policy into its own execution means for many years and which provides a high degree of independence and quality in the provided service. Mar del Teide (1992), Mar del Aneto (2002) and Mar del Enol (2010) floating docks are all outstanding works, together with the self-propelled Acanto (2003) dump barge with dynamic positioning.
http://www.fccco.com/documents/265311/321452/Maritime Works

This academic paper refers to them as floating docks, but it also appears to be a translation from Spanish:

The construction of caissons for vertical breakwaters and quays on the Spanish coast has increased dramatically over the last decade. The overexploitation of coastal quarries and environmental constraints associated with conventional mound breakwaters has favored the expansion of the Spanish fleet of floating docks for constructing floating caissons.
https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/do...


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Note added at 36 mins (2018-01-22 16:31:30 GMT)
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I've also found "caisson production vessel"
FCC’s construction subsidiary is building 9 of the 49 reinforced concrete caissons, which will form the foundation of Açu Port. The company chose Algeciras (Spain’s most important port) as the site to build the first components because of its draught since the Açu facilities are not yet prepared to moor the caisson production vessels.
http://thecorner.eu/companies/fcc-to-ship-colossal-component...

After passing customs in Rio de Janeiro, the first five caissons will be towed to São João da Barra and sunk in Açu Port to form the temporary breakwater behind which the Mar del Aneto and Mar del Enol caisson production vessels will be moored.
https://www.nationaldriller.com/articles/88703-spain-s-fcc-c...