Busking on the South Bank

On Sunday 29th July I was asked by two police officers to stop poetry-busking on the South Bank (opposite Tate Modern) on the grounds that 'Southwark doesn't allow busking'. The police suggested I move to Lambeth where busking is apparently not unlawful. Such a regulation seems arbitrary and illiberal. On what grounds can busking be not allowed, if it is not disturbing the peace, or inciting to hatred? How can it be allowed in one borough but not another? What is the legal framework which the council has employed to support this regulation? I have written to Southwark council, and also to Peter John (leader of Southwark Council), and to the MP for Bermondsey and Old Southwark, Simon Hughes, requesting an explanation of this policy.