The benches were suddenly removed from the centre in early June, sparking anger from local residents.
Shoppers criticised the move, stating that it would have a negative affect on older and disabled people using the centre.
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On Saturday, June 26, residents even took their own chairs to the shopping centre for a sit-down protest calling for the return of the benches,
However, LCP said that the benches had been an "obstruction" to the pathways.
MP Rachel Reeves (Lab, Leeds West) and Bramely and Stanningley councillors, Kevin Ritchie, Caroline Gruen and Julie Heselwood raised the issue with the new owners, and have been in consultation with them about bringing back the benches.
In a meeting on Friday, June 25, the councillors and Ms Reeves met with an Associate Director of LCP to discuss reinstating 16 benches.
In a joint statement, Coun Ritchie, Coun Gruen and Coun Heselwood, said: "Prior to the meeting we had submitted an extensive dossier outlining a strong case for their return.
"This covered the equality impact, community concerns as well as an evidence based, economic argument that having benches benefits the centre economically, making the shopping experience more relaxed and pleasurable, therefore improving footfall and spend at the centre.
"This was supplemented by a number of supporting letters from key community organisations.
"While there was an agreement to the principle of reinstating some benches, we were disappointed that the representative from LCP came to the meeting without a definitive response to our proposal, but rather tried to negotiate the numbers of benches proposed down.
"However he did undertake to take our proposal back to his board for a decision."
They added: "The Centre is privately owned but they indicated they are here for the long term, looking to invest and improve the centre and committed to future meetings with us, in advance of decision making.
"We are determined to stand up for and represent the people of Bramley and continue to be deeply unhappy with the current situation concerning the benches in the shopping centre.
"We will continue to update you on our representations, we thank the Bramley Community for their input and support for the campaign."
Previously, councillors stated that they had been told by LCP that the free parking would be reduced from two hours 30 minutes to two hours from July.
They said that they have been told the plans are still under construction, but include more disabled and family pays, but also charging for stays beyond two hours.
This compares with the current 2.5 hours free parking in a 24 hour period.
A spokesman for LCP, which manages Bramley Shopping Centre, said: “The benches were removed because they were causing an obstruction on the common area pathways.
“Any decisions made are done so with the best interests of our tenants and shoppers and we will consider if new outdoor seating arrangements can be made once we’ve had chance to assess the impact of the change.
"However, there is external seating outside Costa Coffee and retailers can request the same by applying to the landlord for its consideration.”