The reply is neither straight forward nor simple as with regards credit applications there are many variables.
You need to take into account your income, all outgoings not just mortgage, loans, cards etc but also utility and house hold bills, and how timely you are with their payments and with regards credit card you just pay the minimum or more than. There are also factors of the credit history of the house itself and others living within the house.
The first thing is I'm guessing with regards the 3 cards you have now you applied for them at the same time and previously only had 1 making it easy to get ( same thing happened to me at the age of 18 I applied for 5 cards not expecting to get any and ended up getting all 5 although that was rather along time ago ). When the check was done for those you only had 1 card and now you have 3 or 4, so when you apply for another card the chances of rejection will be higher as it is not what you owe that is taken into account but your available credit.
To maximise your chances I would transfer the balance from all cards to 1 card, cancel the other cards, give it a couple of months once all the confirmations have come through for the cancellations and then apply for one card to transfer the whole balance to. I would keep the card you have had the longest and keep it clear and for emergencies and ditch the others. I assume this shouldn’t be a problem if you kept the card that had the original debt that was transferred to 3 other cards to start with thus you should still have sufficient credit limit on it to transfer back.
If this is not possible for what ever reason I would talk to your own bank and explain the situation and try to arrange as low an interest rate as possible PERSONAL loan ( do not be tempted to take it out for more than you need ) to clear all the cards, cancel them all except the one you have held the longest and then in about 6 months try and get an interest free card, if accepted clear the loan with your main card and transfer the balance to the interest free card.
The main thing to take into consideration is that a rejection for a credit application is marked on your credit record as such and applying again soon after a rejection for what ever reason can cause alarm bells to ring and another swift rejection. So my advice on this if you are refused for what ever reason give it 2-3 months before trying again
