Although liming the a clay soil can improve the structure by forming clumps, the proimary use of lime is to raise the PH of the soil from acid to alkaline to help grow certain plants and veg. ( Brassicas like slightly alkaline soils for instance ) Most of the clay soils around Marple and Mellor are extremely dense "Boulder Clay" from glacial deposits and are in some cases, almost a geological formation rather than a soil. I would also test the PH of the soil with an inexpensive kit first as clay soils can be alkaline to begin with.
As Mr Myers suggests, a combination of manure and double digging is the best solution , although you will have to work hard to see resulst. It takes time. Add as much organic material as you can , you don't have to dig it in much as natural processes and worms etc will do it for you. Empty pots , old growbags, compost staright on to your beds.
A word of warning , dont lime and manure at the same time , lime raects with the nitogen in manure and you will lose any benefits. They cancel each other out. apply lime in the winter and manure in the spring.