The response of a lean premixed flame subjected to acoustic perturbations is a complex phenomenon that depends highly on the type of flame and the operating conditions. Swirl introduces additional complexities due to the azimuthal component of the flow. In this work, a bluff body stabilised burner is studied under non-swirling and highly swirling conditions by placing a removable axial swirl upstream of the burner. The influence of swirl is assessed in terms of the flame describing function which is the ratio of heat release rate fluctuations response to incoming velocity oscillations and the spatial flame dynamics at high forcing amplitudes. The effect of flame interaction with the wall on the flame response is also explored by considering an enclosure with a larger diameter. It is found that swirl can affect the non-linear characteristics of the flame at medium frequencies (Strouhal numbers around unity) by altering the flame roll-up mechanisms. This is related to the variation of the local swirl number in space and time. For Strouhal numbers that are considerably lower than unity, the effect of swirl is small due to the high convective wavelengths. The size of the enclosure can also change the flame response characteristics, specifically for large forcing frequencies. With a small enclosure, where the flame interacts with the wall, the flame break-up is more significant and the vortex formation is interrupted. This does not happen when the enclosure is enlarged and it can affect the non-linear behaviour of the flame.