Southwark Council's planning committee unanimously voted to approve the application, submitted by Aviva Investors and Galliard Homes, at a meeting on Tuesday night.
The development at Cantium Retail Park will include 237 social rented homes and 126 for shared ownership.
The scheme includes space for shops, cafes and restaurants and is expected to create 580 jobs. It also provides space for a "destination" cultural facility such as a theatre or cinema.
Jonathan Welch of the Southwark Law Centre warned councillors that there was insufficient evidence to support the loss of retail space, and raised questions about the impact on adjacent industrial sites and whether the scheme is deliverable in economic terms.
Mr Welch suggested that the scheme's benefits could be achieved without such high-rise towers: "A 48-storey tower is very tall and inappropriate. There are only four residential buildings in London that are taller than this."
The meeting heard concerns about the largely car-free development – with parking spaces only for wheelchair users and retail workers – and the environmental impacts of building at such a height.
Historic England had also raised concerns about the development's impact on the "picturesque qualities" of several historic sites including the Caroline Gardens Conservation Area.
But the need to build homes outweighed the concerns.
"I'm very conscious that we are dramatically changing the landscape along the Old Kent Road," said planning committee chair Cllr Martin Seaton.
"We have certainly made a number of decisions that will have a long-term impact on that landscape.
"I am very conscious – having been to New York and great cities of the world – that this is a fact of life.
"If we are to have any chance of addressing the housing crisis ... it has to be upwards."
Cllr Seaton added: "whilst this is not a perfect scheme, I have not yet encountered a perfect scheme."
Existing Cantium Retail Park tenants Pets at Home and Halfords will be included in the development.
B&Q has objected to the planning application but the developer has since agreed to hold discussions with the DIY firm about making space for a smaller store.
The "car-free" development would encourage residents to cycle and use public transport, according to council documents, with the site along the possible Bakerloo line extension route.