A report from the council said the air-conditioning would have minimal impact on the significance of the listed building and the noise from the units would comply with the borough’s criteria.

^{The Beckhams submitted a fresh application for air-conditioning in February (Charles Brice LTD)}

Jonathan Bore, the executive director for planning and development, said: “The proposals would safeguard the special architectural and historic interest of the listed building, would preserve the character and appearance of the conservation area, would preserve the living conditions of neighbouring occupiers, and would have an acceptable impact on trees.”

The Beckhams bought the property in Holland Park for £31.5million in cash in 2013.

With the help of designer Rose Uniacke, they are restoring the Grade II listed mansion to its former glory.

^{Plans submitted to Royal Borough of Kensington and Chelsea Council included interior photographs, including one of the former swimming pool}

It is a slow process with photos sent to the council last year showing the house had been stripped ahead of its overhaul.

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When ready, the property will have six bedrooms, a gym, study, office, playroom, cinema and large drawing room.

The first floor will belong to David and Victoria and boast a huge bedroom, an even bigger dressing room and an en-suite bathroom.

^{The Beckhams have hired designer Rose Uniacke to oversee the project (Charles Brice LTD)}

There is also a separate mews house at the foot of the garden, which will also be renovated.

One local described the plans as a “prudent and sensible set of alterations which will add to the value of the property over the long term”.

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A neighbour nearby added that councils should be encouraging the likes of the Beckhams to “restore these beautiful houses to their former glory”.

Estate agents have estimated the property could be worth as much as £42million when completed.