The bodies of Leo Tompsett, aged five, and his mother Cheryl, 42, were found by coastguards on Monday morning near Eastbourne.
Leo’s father has paid tribute to him, saying: “With more sadness and hurt than anyone can imagine, our precious Leo who was our shining light, our brightest star has had his life cut short.
“We all miss him an amount beyond what anyone else can imagine and would request that our privacy is respected at this very difficult time.”
A Vauxhall Corsa was found at the scene and was being investigated by police in connection with the deaths.
The coroner has been informed of the deaths.
Detective Inspector Simon Dunn said: “Our investigation continues in this tragic case, however, at this time, there is nothing to suggest that anyone else was involved in their deaths.
“Detectives are in the process of piecing together the last moments of their lives.”
:: Anyone with information should contact Sussex Police with reference number 1294 of 17/06.