It will be delivered by leader Cllr Elizabeth Campbell at the full council meeting, which takes place at Kensington Town Hall in Hornton Street, Kensington at 6pm.
Following the update, members of the public who have a strong connection with the borough and who did not speak at the previous meeting, can ask questions.
Anyone who who wishes to do this is requested to notify staff of their intent on arrival at the town hall.
Away from Grenfell, the meeting will look at various home care, Universal Credit, the regeneration of Warwick Road and Silchester Estates , and home care
A debate motion will discuss whether a 20mph pilot scheme scheme should be introduced in St Helen's ward in North Kensington, due to " an increase in accidents and speeding vehicles and high level of air pollution in the borough".
The meeting will also include questions posed to members of the Cabinet from other councillors.
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likely to focus on the progress of the Grenfell Tower response efforts.