It is quite possible that your neighbours are unaware of the effect their "open house" is having on you.
You have to live with them, so the last thing you want is to upset them - think how much noise they could make if they were actually trying to do so!
So what you need is mediation. Record some of the noise from inside your house, to use if necessary. Drop them a very polite & understanding letter along the lines of "I'm a parent too and I know how the volume can increase when kids are having a good time, they are all so lucky to be able to play in your well-equipped garden" but could there please be some quieter times? Try and imagine the boot on the other foot - how would you like to be asked to restrict your children and their friends? Could they agree to send them all home at 6pm for example?
I am a parent, I understand they make noise, but I don't enjoy the yelling and screaming that comes from the nearby school, howevermuch I like to think they are running around and letting off steam between classes.
Most councils have a mediation service, so if polite approaches don't work, you may have to contact the council.
Good luck.