Hello Freddy.
I have found the same John Wood that you have a warrant number for in the Alphabetical Register of Joiners on
page 414. This record contains the people that recommended the officer and when the officer left the force. I don't know how useful these two pieces of information are but they may be worth a look.
It has him as resigning on 10th Feb, 1840. And the addresses for the referees appear to be Mr. Folkes of 9 Suffolk Street and Mr. Bradshaw of Camden Town.
There aren't many records that would otherwise detail conclusive things like the year and place of birth that I know of - others feel free to correct me if I'm wrong.
As most of my work has been to photograph and make available a transcript of these documents I can only help that much. You could try the Metropolitan Police. There is a form on the Friends of the Metropolitan Police Historical Collection (
FoMPHC) website. They have some sources that aren't in the National Archives and have access to a greater database of information so might be worth a try.
Yours, BarnabyP