I am afraid that the way the bank has to look at it is that in order to consolidate the debt you have to first borrow more money and it is this total of the new loan and the debt to be consolidated that it likely too much for your risk profile and this is why they have said no. It doesn't matter that you are planning to to pay one debt weith the other, the fact is you have to double your borrowing in order to do this...even if only very short term.
Speak to your bank and see if they can let you borrow a smaller amount, if you can then use this to put your debt plan into action then you may be able to borrow the remainer of what you need later down the line when you have cleared some of the existing debt.
Good Luck