Hibiscus syriacus flowers from August to October and there are several different forms to choose from. Hardy fuchsias will start flowering a lot earlier but will still be in full flower in September.

There's an anemone called A. japonica 'September Charm", though it isn't a shrub. Hebe 'Autumn Glory' is a later flowering shrub, though it usually starts in late summer and goes on till late autumn. Nerines are bulbs which flower late, usually October, sometimes earlier, depending where you live. Hydrangea paniculata 'Grandiflora' is another late flowering shrub, starting in late summer.

Hoheria sexstylosa 'Stardust'. Beautiful late flowering evergreen shrub that should be better known.