Your definition of the best will depend on factors like how far you (or your child) want to focus on tennis alone, and how important you think it is to develop other areas too. The main thing is only to look at places that are connected to the Lawn Tennis Association (LTA) since they will monitor quality.
As well as tennis academies, a lot of people also consider high performance centres (HPCs). These are solely for sports and your academic eductation is carried out elsewhere, whereas a tennis academy includes mainstream schooling.
Some academies, like Dukes Meadows at Chiswick, provide an individual study programme for each student, with help for learning difficulties etc, as well as full tennis and fitness training. Others such as Gosling Sports Park offer a distance learning programme. It's important to look at an academy's academic record as well as its sporting achievement, since everyone needs a general education as well as specialist training.

To get started, you can find a list of top UK academies here.