Thermocrete is the answer.

Thermocrete is a revolutionary process which allows your existing chimney to be relined without any construction work. The material used for this is Thermocrete B2 a lightweight but incredibly strong monolithic refractory castable. It will restore your chimney stack to perfect condition (making it stronger than new), completely curing existing damage and preventing further deterioration. Thermocrete is impervious to flue gases and acid attack; it also has excellent insulation properties.

The dangers of faulty flues

Whatever form of heating you use - coal, gas, oil log burning, etc. - an efficient chimney flue is essential to you... for both economy and health. Inadequate insulation causes condensation, which combines with the fumes to produce sulphuric acid. This attacks the brickwork eating into the mortar resulting in dangerous joint leakage, eventually leading to the total collapse of the chimney stack.