The wrong location and the size of the bedrooms are among the reasons why accommodation has been refused by residents on the Royal Borough's housing register.
Since the start of the year, 13 people have turned down offers of housing from the Royal Borough when places become available for housing association-run homes.
The borough has 2,400 people on its register who are waiting to be allocated housing, while 203 have been offered accommodation this year.
Affordability concerns and the fact that the person being offered the housing is too elderly to move have also been given as reasons for turning down offers.
Nobody has turned down two or more offers of housing in 2013.
The borough transferred all of its council housing stock to sponsored housing associations in 1995, but has retained nomination rights to allocate residents to a percentage of the properties.
Its register is for people with a local connection and a demonstrable housing need.
The figures were obtained through a Freedom of Information request.
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