The Orange mobile company intends to apply to install an 11.5 metre mast on Petersham Road, directly opposite the entrance to the Russell Primary School.
The company has to apply for planning permission for the mast because the site lies in a conservation area.
Council leader David Williams, who represents the Petersham ward, said: "I am horrified at the idea and intend to oppose it.
"Richmond Council has refused planning permission and deterred mobile companies from erecting aerials near schools or on school grounds.
"I am sure we will continue to do so."
New guidelines restricting the siting of mobile phone masts near schools or residential areas are now being considered by the Government.
Richmond Park MP, Jenny Tonge, said: "At present councils have very few powers to control the siting of such masts, in some instances the masts don't need planning permission at all."
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