Wanting to get a loan to consolidate my debt

So due to my own stupidity and a healthy helping of manic depression, i managed to build up 14k in credit card debt, however i'm in a better mental place and have been trying to pay it off as quickly as i can, i make about £4-500 worth of payments a month.
I was looking and realised, if i can get a loan for 14000 then with a good apr i could carry on making the same monthly payment but everything would be paid off in 3 years, however when i try any loan checkers etc.. i'm basically "not eligible" for any loan other than ones with a higher apr than my current credit cards.
I suspect it's because of my monthly income being too low as my credit score is good and i've never missed payments etc.. but i just wish there was a box that said "i'm currently paying the same or more a month that the loan payment would be, and i'll be using the loan to pay off the things those payments currently go too, i've never missed a payment so i can afford it". Tbh i thought that's what saying i was applying for "debt consolidation" would do, but apparently not.
Sorry if this isn't the right place to post but just needed to vent a bit, kind of frustrating to finally be trying to sort myself out but it feeling like those that could help are saying "no, you can't pay it off as quickly as it could be possible, you have to have most of your monthly payments go towards interest" I know i have no right to get a good apr loan etc.. but like i said... frustrating.