I sympathise with you, matey.
Anyone who wants to join up and serve their country (lets' not make this into a political thread!) should be encouraged to do so, in my opinion.
However, the UK Armed Forces traditionally recruits from the younger end of the population. Dont get me wrong, people with a 'few years on' are an asset to the Military, but the situation you describe does not fit with the policies the recruiters are given to work with, around, etc, which can be quite old (traditional!) in my personal opinion.
When they say they 'can't' recruit you they mean because applicants are financially vetted. Debt leaves people open to or at risk from blackmail, subversion, etc. There used to be a rule of thumb in terms of how much of your pay you are allowed to spend on debt each month! Remember, if you were 16 or 17 and had never lived away from home, earned your own money, etc, the Military would have a duty of care over you.
I would say look at ways and means of meeting your obligations (previously discussed) and go for it! Having said that, does you're mum not need you around?...not away for months with the Royal Navy!
My opinions do not neccessarily reflect the opinions & Policies of the UK Armed Forces.