Fast forward 12 years. What sort of young adult do you want to see?
Someone who is happy and confident and in control of their own destiny. Someone who is educated and with good social skills who is capable of self motivating. Children like this emerge from a range of schools. Having a good crop of qualifications is only part of the picture, and though they help, people without them can also succeed. Pupils at most if not all of the destination schools from your son's current prep will achieve strong results, and to a large extent differences will reflect difference in intake. Supportive parenting is also a big factor.
The very academic London schools are fantastic for the right child, but can be a less than happy experience for the wrong one. It is as much about personality as intelligence. Some children need confidence and will do better in a school where they are top of the class. Some are simply less studious and may resist, what is for them, an overly academic culture. You need to choose a school not simply for the results but whether it feels right for your child.
Making a move now to help ensure you get a place at 7+ in a school that then goes through to 18 will limit your choices. Great if your child is bright and the culture the school offers suits and engages him. But awful if he is then at the bottom of the heap, and spends his whole childhood struggling to keep pace, with less time to gain other and important non academic skills and experiences. At 18 he might have the right crop of GCSEs/ASs/A2s but is unlikely to be the confident, personable and motivated young adult you wanted to see.
By all means try 7+, and ensure he is prepared to a reasonable degree. But after that let the 7+ school decide whether he is right for the school at that time. Moving schools so he can be better prepared runs the risk that he spends the next year or so, under pressure to keep up, squeezes into an unsuitable school and remains under pressure through the whole system.
Also talk to young adults emerging from their schooling. Ask them what they thought was important. As it happens my son is at one of the very sought after London secondaries. He applied for 13+ from a fairly relaxed Prep, got in and has really enjoyed it. He has friends at a range of other schools who are also doing well. When he goes to University I hope and expect he chooses his friends on what they have to offer (shared interests etc) rather than the school they went to.
Meet some of the school run mums in a decade's time and the conversation may well be about how to keep their sons motivated. Being in the right school for the child rather than the "right" school goes a long way to avoiding the problem.