What age does Private Child Maintenance Agreement stop

Hi All 🙂 
Hoping anyone could share some advice on the following….
My partner has a child (consequence of a one night stand many many years ago!). A private child maintenance agreement was mutually agreed upon when the child was born. I believe that there may have been a basic handwritten note created and signed by both parents but this agreement has been pretty much a verbal agreement throughout the years.
Background on the situation and character of the mother, my partner has been there since day one, paying child maintenance and any additional costs for school, trips, birthdays / Christmas, clothing / etc etc with him looking after the child Fri to Sun every other weekend and when the mother went on holidays. He of course wanted to be in the child’s life as much possible even though this has been challenging at times. As the mother is notoriously difficult and spiteful at times stopping him from seeing his child for no real reason. This case has never been through any courts or CSA as my partner has always tried to be amicable for the child’s sake. To paint a clearer picture the mother….she has 2 other children (younger than my partners) who we know for one of them, she has been hot and cold throughout the child’s life with not letting the father see them. Again he’s always paid his way and taken it as far as courts numerous times, where they have court ordered and demanded that there is no real reason for the mother to stop the father from seeing his child. But she continually breaks the court orders and there is no punishment for that, so he’s back to square one. Sadly he hasn’t seen his child for about 5 years now since they were around 10 years old. He always hand delivers birthday / Christmas cards through the door for her but the mother just spitefully pushes them back out. 

Anyway….about 5 years ago the mother got with someone and fell pregnant quickly again but actually had a short term relationship with this guy (he ended up leaving her as she cheated on him).At the time when he moved in to the family home, both children (my partners & the other father I mentioned above) surprisingly all of a sudden stopped all contact with both fathers (which wasn’t surprising!), saying that they didn’t want to see them anymore etc etc clearly it was the case the mother was trying the phase out both fathers as this new guy was on the scene. Obviously this massively hurt both fathers but they still continued to pay their way and message their children asking when they could see them. Which they would either get ignored or rude blunt responses from the children directly. 

My partner hasn’t seen or spoken to his child for 4 years now and has pretty much given up thinking he will ever see her again (even though she’s just 15mins down the road and not like the other side of the world based on how the mother & children behave towards the father's). Both fathers and the grandparents (who also get given this cold blunt behaviour and haven’t seen them for the same length of time as the fathers). 

My question is….my partners child will be 19 this year and will be finishing A Levels. We have no idea what their next plans are as they have stopped all communication with my partner and his parents - even though they still message her which gets read but just gets plain ignored. 

Does his child maintenance stop this year for the 19 year old child? From research we believe so especially where this is a private agreement (as it’s less complicated than CSA agreements) and where the child would have officially finished education August this year and will be turning 19. Plus we know they work but this may only be a few hours a week inbetween school. 

Before any sarcastic comments are made this isn’t just another father just trying to get out of paying for his child. It’s good fathers being tormented by a mean mother knowing how to abuse the system. Ideally he would love to see her and have normal relationship with them but unfortunately the mother’s bitter spiteful ways seemed to have rubbed off on to them and decided to take that road of being unesscessary spiteful to the fathers and grandparents and cutting them out completely. My partners child is an adult now and knows better and the other is nearly an adult and also knows what is right and wrong. If the relationship was normal than he would continue to support his child if they were thinking about university etc but give and take how mean and spiteful they have been over the years he just wants to cut ties as it seems that is what they want over the last few years.