Plans had been lodged by from Apex Investments Ltd to demolish the former Henry’s Restaurant building at St Paul’s Square – and put in place a four-storey block of flats with commercial space on the ground floor.
The plans had been opposed in an online petition signed by 77 people – including residents of nearby St Paul’s Court which would stand adjacent to the new development.
Concerns included a loss of privacy and light at the existing homes which include a row of townhouses.
Speaking against the plans, Maggie He, a resident of St Paul’s Court, said: "A four-storey building will be imposing on all our rooms.
"It will be overbearing and have such a severe impact on light, noise and privacy that it will literally make us claustrophobic in our own homes, hence our repeated objection."
Another objector said during the meeting: "We did ask for various meetings with the planning officer to come and see where we live, and we are owner-occupiers, and those were never taken up.
"It is going to affect us massively. We bought that property for some considerable expense."
A speaker speaking in favour of the plans said: "This is a brownfield site in a highly sustainable location.
"We have policies confirming residential developments of up to four stories as proposed are acceptable.
He said the proposals achieve an appropriate balance between "safeguarding privacy for residents" and allowing a development which reflects the "character of the conservation area".
Presenting a report to councillors, a planning officer said: "We need to understand that there are heritage benefits to back-of-pavement development.
"There are heritage benefits associated with this and no harm has been identified by the conservation officer as part of this proposal.
"The benefits of having something more of the character of the Jewellery Quarter, that more reflects the history of the site and contains the street better all weigh in favour of the scheme."
The committee voted in favour of the plans by ten to one with one abstention.