Progress variable approaches permit the efficient large eddy simulation (LES) of complex industrial combustion systems, where assumed shape filtered density functions (ß-FDFs) are widely used to account for subgrid scale effects. In this study a new modelling approach for the LES of partially premixed combustion is introduced, which is based on top-hat filtered premixed flamelet-generated manifolds (TH-PFGM) which are consistent with the LES methodology. Due to the top-hat filtering the resulting lookup tables require fewer dimensions than conventional ß-integrated tables, permitting a low-storage representation. In the present paper TH-PFGM is applied to a lifted swirl flame in a model gas turbine combustor. The paper presents the underlying TH-PFGM modelling theory, its extension to any number of dimensions, and simulation results from the LES of the model combustor. Results show that TH-PFGM accurately captures the flame lift off dynamics governed by a low frequency penetration of the flame into the fuel supply, which leads to fluid expansion and in turn flame lift off. The statistical data for flow and species concentration fields from LES are in good accordance with the experimental evidence, as well as results from a comparable LES study.