West Somerset County School OTC became Wellington School Somerset OTC in 1914.
The School Cadet Corps can be seen here wearing SLI VB collar badges in their caps and the officers are wearing full sized Bx SLI cap bagdes:
The Wellington badge has that title on it so unless the school was operating with 2 names it is unlikley to be that one. There was a West Somerset County OTC Shoulder title.
http://www.oldwellingtonians.co.uk/f...aspx?S=kp8rg69
My assumption is that on the creation of the OTC in 1908 the Cadet Corps continued their association with the SLI and continued to wear SLI TF badges. I suspect this was initially still on side caps so collar badges would have continued to be worn.