Kent (including London Boroughs of Bromley and Bexley) and Buckinghamshire have grammar schools.
If your son is 10, when do you arrive? And when is his birthday?
The 11 plus exams for grammar school entry are usually held the 2nd week in September for entrance to the schools the following September. You will find details of the exams on the local authority websites (Kent County Council, Medway Borough Council, London Boro of Bexley & London Boro of Bromley).
I only tell you this because you may well research the 'great' grammar schools in say Kent, Bexley or Bromley and then discover you are simply too late to gain entry anyway.
Chancery Lane is walk able by the way from Charing Cross Station or Cannon Street station in 20 mins. And would save you near on £1000 a year on underground fares. If you get a mainline train into London this is one price and if you then travel further in London using the buses and tubes, this is another price on top. (all on one ticket though)
For Charing Cross & Cannon Street, you are looking at SE London (also recommend Blackheath) London Boro Bexley, parts of London Borough Bromley (Bromley North Station goes here, South doesn't) and vast swathes of Kent.
You can also travel into London Bridge station from most of Sussex and Surrey and then change onto a train into Charing Cross/Cannon Street.
You need to think long and hard about your commute, how long, how much you think it is fair to spend and how quickly you can get home to collect the kids!