For French paper Le Monde, Marc Roche accuses Mr Cameron of remaining "vague" about the "fundamental point" of what would happen if France and Germany refuse to meet his demands.
The three allege they were then taken to the desert and then to Williams' and Cameron's hotel, said Marc Calcutt, who had earlier represented them on behalf of Reprieve.
Representatives of Reprieve have seen each of the men since their arrest, but Ms Higham and lawyer Marc Callcutt visited Dubai recently and made two unsuccessful attempts to see Mr Cameron and Mr Williams - on 25 and 27 March.