Out of curiosity, how are you defining central London? Are you referring to the City, the West End or zone 1 as a whole?
The joy of central London is that at the very least, one is always within touching distance of at least one tube station not much more than a five minute walk away. If the tube is a ten minute walk, that would suggest it is not well-placed (but then I am spoiled where I am as I have four tube stations, two Crossrail stations and a mainline station all within a five minute walk)! That said, ten minutes is not an unreasonable walking distance at all, particularly as some locations in W1 and SW1 are some distance from the tube and are popular with incall hosting service providers.
Other things to consider is if the flat is easy to locate and does it have access to (metered) parking too?