"They have a dedicated swimming coach which is rare." Really!?
The level of swimming at the school will depend on who the coach is and the amount of time timetabled in. Without a clear swimming specialisation, which Plymouth, Millfield and Mount Kelly all have, you are unlikely to get to the standard needed.
If you re serious about the doing the 14-18 hours a week training that a competitive swimmer will need to do, you probably need to identify a school whose facilities are used before and after school by a good club, with good coaches. The swimmer then has the advantage of being on site so, say, able to get homework done before evening training. Such schools will probably have strong swim teams, so I would be tempted to look at which schools have consistently done well in ESSA competitions and work back.
In terms of the "big three" I am not sure any are seen as particularly academic. Anecdotally I have heard of several Millfield swimmers being quite unhappy, but this was girls not boys. I have also heard that you probably need to be very very good at Plymouth (which is linked with Plymouth Leander swim club) to get full coach attention and priority for pool time.
I have not heard of Sevenoaks being particularly strong, though accept PettsWoods word that they are. Whitgift, which now offers boarding, would be worth a look. They, like Sevenoaks, are also very good at hockey.