A good way of measuring is by calculating the districts (or boroughs) in the central region of London. This includes the boroughs of Westminster, Camden, Islington and Tower Hamlets (which comes to 38 square miles).
With regards to the 'centre', neither Swiss Cottage (in Camden borough) nor Poplar (in Tower Hamlets) 'feel' very central to me.
Another possible way of calculating the centre of London is by using the 'gates' of London.
In gates I'm thinking of Aldgate, Notting Hill Gate, Lancaster Gate etc. But admittedly, the precise measurements between these gates aren't exactly easy to ascertain. Anyway, no describable borders or boundaries can truly be agreed upon as over the centuries, London has grown, constantly taking in more territory.
However, from Aldgate (in the East) to Notting Hill Gate (West) is 5.6 miles. From Highgate (north) down to the Thames is a similar measurement, thus 31 square miles.
Maybe someone with specialised knowledge would be able to give a more precise measurement.
However, some people mistake 'central' as being the West End (Oxford Street, Picadilly Circus etc).
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