My girlfriend is in a very similar situation, she's been at uni for a few years finally got her PHD and gone to hundreds of interviews and they want experience! It's just a joke how the system works these days.
Going into the Navy will take you away from your family the only advise I can give is keep trying and don't give up, keep getting the interviews and at the interviews tell them you don't have the experience but you have the education you've spent time and money getting educated and the only way I will get experience is by getting a job and that's why I am here!
I would hate to be in a position like this I considered doing a Uni course but then there are so many who graduated then there is nothing there afterwards. Just debt and no work.
Times are really hard in the UK especially getting a job you'd be better of spending every day searching for jobs, getting the interviews and hoping luck will land your way.