Izabella I'm sure it is. We know people who have moved quicker and some have taken much longer. It all depends on personal circumstances. However, the OP is asking for advice about her circumstances so perhaps being pragmatic is her best option. She needs to look at her options and her buyer's options to decide what to do.
Do you still wear you original wedding and engagement ring
To think that London, or anywhere else for that matter, does not belong to any one demographic