In the Royal Marines it's 15 years and 9 months according to my paperwork from when I first visited. In the Army there's a junior leaders course which I think you get put on if you apply when you're 15 and 7 months. This allows you to progress through NCO ranks faster but it's different for the Royal Marines.
Yeah i had something similar, young boy came in with his paper work only to say his mother would not sign them nor would the place that is looking after him as the don't have guardian rights over him, dunno the full story there but heart went out to the little guy, he looked so demoralized over the whole thing.
Normally underage applicants are advised to join the local Cadet units if they haven't already as they give a better insight. They also give those seeking leadership skills, the ability to get a bit of experience - particularly useful when applying to join as an Officer.
The biggest problem is many people tend to view the cadet organisations with disdain- feeling it's "not cool", yet they actually contribute hugely to the recruitment of successful applicants with realisticly managed career expectations.