I had a home improvement loan, twice, and a car, twice, had to remember what I'd written on the previous form though, and be a little bit careful!! "Credit card consolidation" loan also works as a reason.
So agree with that advice.
However, it did strike me that you haven't started flying yet, you say you don't understand why you weren't offered a loan, earning £50k between the two of you, but then you say you have no savings and your credit card's up to its limit.
Now I am the last person to say this really, but, if I were your bank manager I think based on what you've said, I would say no too. You obviously have no spare cash each month and currently spend more than you earn, and now you want to go and commit yourself to spending even more per month on repayments so that you can go and get a PPL. How are you going to keep it current? And I really hope you are not considering a commercial course at this time? I suspect if you pay off your credit card and saved around £500 that you would get the loan.
Sorry for the reality check.