I don't think there is any brick between my party walls

Well adding a layer of insulation would help reduce the noise levels between the two properties. Depending on your wall I could add a layer in between the timber frame and then another layer on top increasing the effectiveness of the insulation. Having a look at the property would determine the best solution.

Hi I’m sure there will be a brick wall there but as mentioned insulation would drastically reduce the noise transmitted through. British gypsum also do a sound board to help combat this. This can be fixed same ways as any plasterboard. Hope this helps