European junior champion Dixon was leading with one round to go, but was overtaken by his Great Britain team-mate Matty Lee, who produced a stunning last effort to score 90.60 points and take gold.
Lee finished with 431.40 points, with Dixon on 417.60 and Noah Williams taking third with 417.50.
Dixon’s second, third and fourth dives all scored 72 points or more, but his opening armstand back triple somersault effort and his fifth round reverse three-and-a-half somersault tuck dive were slightly below par for him, scoring 59.40 and 66.30 points respectively.
There was a good performance by Dixon’s Plymouth team-mate Aidan Heslop, who came fourth with 402.10 points. Heslop saved his best for last, scoring 79.20 points for his final dive.
Also on the final day of the championships, Dixon’s cousin Shanice Lobb came sixth in the women’s platform final with 262.70 points.
The women’s final was won by Leeds’ Lois Toulson, who scored 327.90 points, with her team-mate Ruby Bower taking silver with 310.65 and former Plymouth Diving member Robin Birch securing bronze with 310.00 points.
In the women’s three-metre individual final, Plymouth Diving’s Kayleigh Sinclair came seventh with 236.20 points. The title was won by Katherine Torrance, who finished more than 60 points ahead of the rest of the field with 328.65 points.