As far as I am aware only two story papers featuring Lynwood School were published. Chums of Lynwood appeared in 1949 and Fourth form at Lynwood in 1950. Both were from by JB Publications.

Chums of Lynwood contained a long story featuring the boys of Lynwood and the girls of High Lynn. Thanks to Nandu you can download the story paper here.

Fourth Form at Linwood contains a complete story of Lynwood school and a couple of short stories also by Hamilton. A Tipton School story  features a character by the name of Bunker Bates and the second story features Mick of the Spindrift, a Ken King type of character. I'm not aware of either Mick or Bunker appearing in any other publication. Thanks to Michael B you can download the story paper here.