@nwLondonDad we are local and went for Habs over NLCS but personally would not recommend one particular nursery specifically for NLCS.
When visiting nurseries, look at how they teach children, which schools children tend to go to and my personal experience would be to go for a nursery that is familiar with prep schools and 4+ as a whole, not a specific one. They will be able to honestly guide you whether your child is suited to school you want and also suggest alternatives if that is not the best place for your child.
You don't say how old your child is but the most important thing in my opinion is what parents do with their children and this starts from a young age. These schools are not looking for children that are reading and writing at 3, they want children with developed gross and fine motor skills, imagination, an interest in learning, willing to take part in new activities. Imo these are all things we should be doing with our children from early on.
My children have both had access to scissors and knives (in kitchen setting for latter) from when they were 2 but shown safety and supervised appropriately. At 4, my eldest was able to chop a potato unaided with ease. We encourage them to run around, climb trees and high frames at the park so they learn their limitations with us there. We also do sports such as football, gymnastics, yoga, dance (some taught, some at home via YouTube). When reading books, we look at pictures and describe what is happening, consider how the characters are feeling, predict what may happen next, make up our own end to the story....
If you are doing all these things and they are capable, they will get the place. A knowledgable nursery is good with advising you where is best and writing reports for the schools (I have seen some shocking ones which really do not do an excellent child justice) Some children are not ready at 4 and that is fine, they will get there in their own time.
If possible, try take them to drop off classes so they separate with ease for assessments but schools understand that may not happen and they are still little.