Mmm,
Heard banks were been tighter on current accs (especially during the Halifax exodus) though it theoratically shouldn't be a problem if you didn't apply for any credit facilities such as an overdraft.
Are you back to full time work with no more debts to pay off? If it's not good here then that might be part of the reason you were declined i.e. they don't view you as a potential valuable long term customer.
Check out the AAM best buys for current accounts. Don't worry about the problem too much until you exhausted all the options i.e. try BOI, AIB, NIB and PTSB.
It's a shame if you can't get UB as its one of the better current accounts from a fee perspective.
That said if it really does get desperate... perhaps you can get a "student" account? As far as I know the bulk of student accounts can function like current accounts minus a debit card (get atm card instead). Mature students aren't that rare in these times.
Another passing thought is this you could open one of those crappy on demand savings fee free accounts (like .010% interest) from one of the big two (AIB or BOI). You should be able to make lodgements to these accounts just fine (do some research before hand online) though you'll have to withdraw the old fashioned way in bank.
For DDs can you handle these bills through the post office / bill pay?
Anyways jumping the gun here, try the main options first before going to improvisation.