The Cockburn Association was among objectors who said the proposed mast in Beaufort Road would have a detrimental impact on the conservation area.
Vodafone and O2 said they had explored 16 other possible sites nearby but none were suitable.
A report by planning officials said the replica telegraph pole would not fit with other street furniture because there were no other telegraph poles nearby and the plan to site the mast near trees would do little to reduce its visual impact because the trees were deciduous.
A total of 14 objections were received. Officials have recommended refusal of the application, saying the mast would be an “unusually intrusive feature” in the area.