Mr Gibson, who is well known in the area for campaigning to save his local library, frequents Dulwich and Sydenham.
Friend Joe Duggan, 48, said: "Robbie's family, his friends, and the wider Crystal Palace community that value the great work Robbie has done as a library campaigner, would just love to know that he is safe and well.
"We are getting increasingly concerned.
"This is out of character. Robbie is such a positive and enthusiastic campaigner who gets things done in the community. It's no surprise the community has responded the way it has to find him."
In April, he played a leading role in the Carnegie Library Occupation in Herne Hill in protest at Lambeth Council’s decision to shut libraries and reopen them as healthy living centres.
He is described as white, around 6ft tall, with a slim build and grey hair.
Mr Gibson wears black-rimmed Prada glasses and is possibly dressed in a blue or grey t-shirt with green or brown khaki trousers.
Anyone with information on his whereabouts is asked to call police in Lambeth on 101 or the charity Missing People on 116000
