I am not entirely sure whats available to young chess enthusiasts that you feel will be encouraged by further development, you would have to get in touch with the people involved and my contacts I will give below so you can ask them for further information.
I warn you now affordability of some of the training can be an issue, a good youth coach can ask 200 pound an hour especially in London but if you dont want to spend alot on some top notch one on one training then a group session online can cost as little as 20 pounds per hour i think i am just guessing. The lessons can be with a grandmaster ( tend to be the most expensive) down to a International master or someties even a fide master but dont think grandmasters are the only ones who can teach your child effectively. My best coach was an international master(i wont give details because we lost touch).
If you want to travel to southport Nigel Davies is a top grandmaster coach at reasonable prices but he specialises in online training in groups, google 'tiger chess Nigel Davies'. try web address https://tigerchess.com
Adam Raoof is an ex club secretary of Hendon chess club in london and runs the kensington rapidplay and golders green rapidplays amongst other tournaments- he has extensive contacts with chess coaches in london and will be able to provide details of whats available- of course london is a too far to travel ordinarily but I am sure theHendon chess club provides online coaching. his email address is firstname.lastname@example.org
if you want a fully expensive coaching please get in touch with jon speelman he coaches online(yes the world famous chess grandmaster) it is about 100 pound an hour though but its worth it.
There is the internet chess club but be carefull to check the junior tag when registering because otherwise it has a sophisticated chatting service which is disabled with juniors. web address:- https://chessclub.com - there is a fee with this site.
'Chessable' is another site for training some free, another site 'chessbase' provides the fritz(playing program), chessbase( chess database and analysis tools, program), and fritz trainers(using chessbase to teach chess with video, chess board and analysis tools, they are on a dvd rom).
The most popular playing site is www.chess.com but again be sure to select junior option to disable chat.
a site you may be interested in for children i have been informed about is 'chesskid' its a free and fully protected site for youngsters, parents and coaches to play and learn. https://www.chesskid.com/
contact myself at email@example.com or dave (email on the contact page or here)