At Thursday'sÂ transport and traffic meeting Cllr Lynne Stagg, the head of transport, approved officers' recommendations to establish the FH zone at the north of Twyford Avenue.
Only residents with permits will be able to park on the road between 2pm and 10pm, with the aim of deterring people who were taking up spaces while using the nearby Mountbatten Centre.
But Nelson ward representative Cllr Ian Lyon felt the process was unfair to others living nearby.
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In his deputation he said: 'The trouble with these parking zones is that they are great for the people who live there but awful for the people who don't.
'˜Many residents who come to me feel dispossessed and feel the system is unfair.
'What I would like the cabinet member to consider is by all means make it a parking zone but also at the same time introduce a full consultation of the whole area.
'˜I have heard from a number of residents who are tearing their hair out because they are unable to park.
'And then you are telling me it only costs Â£20 a week to operate making it self-funding.'
Nikki Musson, the council's transport planning officer, addressed his concerns.
'Twyford Avenue was identified for survey in 2010 but was put on hold until 2012,' she said.
'During that time Tipner and the area around Mountbatten were rejected. The reason we didn't survey that area was because there weren't many requests for it.
'Tell people that if they would like to be surveyed they need to contact us. It may be possible in the future to survey them.
'The enforcement costs will be small as the process will be similar to the enforcement of the double yellow lines on that road.'
Cllr Lynne Stagg added: 'We only consider zones when residents ask for them. However, we agreed back in July that if any surrounding areas suffer displacement we could survey them.'
Parking permits will cost Â£30 for each household's first car.
There are 18 homes affected by the change.