Hello Pauline, thank you for replying. No, there is no address shown - under the date (23 July 1852) it simply says "found dead in the River Thames off Horselydown." The informant column shows the coroner's details: William Payne, Coroner for Southwark, Brunswick Square, Bloomsbury.
In the burial record for this John Nash (in the churchyard of St John Horselydown) under "abode" it says "Coroner's Order." Perhaps his family never even knew he had been found? But if his address or family were not known to the authorities, I wonder how they knew he was John Nash aged 42?
From their general background I don't believe the family would have been too poor to claim his body and bury him; and I have located my John's wife Ann Elizabeth Nash in the 1861 census, where she is described as a widow, "Fundholder," visitor of a (so far seemingly) unrelated family in Ramsgate, Kent.