Yes if they have a figure that he owes they will chase him for it despite your child being over 18 as it is owed.
I had the same, £1000 in monthly payments over a year when my son was 22, when up to then not a penny!
Child Maintenance Service had this amount down as arrears and at some point managed to get an attachment to earnings and get it paid. So it will depend if according to them that is the full amount or a payment toward a larger amount. Was there any letter with the cheque?