OP, if you don’t mind me saying this, it’s probably not the best idea to announce your DC as “exceptionally bright” when contacting the prep schools. Find a school first and then let them assess how “exceptional” they are. Please be warned, these schools are full to the brim with pupils whose parents are all utterly convinced of their DC’s “exceptional” abilities
, still very few will get into the likes of Westminster or St Paul’s. Be prepared for a shock.
If your eldest is now 7, he has missed the 7+ entry to St Paul’s (Colet Court) or KCJ. These are considered the “top” boys preps in London because they feed directly into St Paul’s and KCS. If you’re living in South Bank though, these would be a nightmare commute for you anyway.
I think St Paul’s and Kings Juniors (KCJ) May still have a small 8+ intake (maybe a handful of places) but you would be looking at your eldest doing the exams next Jan for entry Sept 2020. No matter how bright he may or may not be, he will need preparation. Make no mistake about this.
As your younger one is still only reception age, I would think it was easier to put them both together in a good prep that will prepare them either for 11 plus entry or 13 plus.
At 11 plus your “top” options would be - City London Boys School, Latymer Upper, Kings College Wimbledon, Highgate, Hampton, etc. St Paul’s and Westminster have a very small 11+ intake, they are more geared to 13+. All good schools, in different areas of London, but you can move accordingly then.
At 13+ (known as Commin Entrance) you have KCS again (smaller 13+ intake these days), St Paul’s and Westminster. Or Hampton. Otherwise it’s occasional places elsewhere. Be warned, many boys from 13+ preps end up boarding.
Have a look at the preps in the area you’ll be living in. Please be warned though, if you waltz in with a 5 year old and announce he is “exceptional” in reception, you run the risk of making yourself and your child into something of a laughing stock. I don’t wish to be unkind, but this kind of thing is naive at best.