Child maintenance comes to an end when, after the young person reaches their 16th birthday, they cease to be enrolled in full-time (= 12 hours per week or more) education in a school (or other educational establishment where they're studying for qualifications not above A-level). For the purposes of calculating the relevant date when child maintenance ends, the summer holiday period of the academic year is considered to be part of the preceding year.
So if your elder son is currently enrolled in a school (even if he's not attending it), your payments will end in the first week in September. However if he's not enrolled in a school, your payments will end on his 16th birthday.
If either of your sons progresses (full time) to 6th form college or to a further education college (and spend two years studying there), your payments would continue until the September after their 18th birthday. (If they spent 3 years at college, while not studying beyond A-level) your payments would end on their 19th birthday.
Chris