Planning officers said the swimming pool and summer house could have been built under permitted development rights, but the tennis court and garage would require planning permission.
The committee heard how, while all four features were built without consent, they did meet local planning policies.
Angie Fitch-Tillett, one of the committee members, said: “I understand the concerns, but it does not intrude on the landscape.
“I think we are all very nervous about this one, but we are here to make a decision.
“We have the officer’s advice and they appear to have covered every angle, but I will propose that this is accepted.”