"I imagine your not paying tax on your rental property if the rental income is falling that short of the mortgage repayment"
Why would you assume that Dublin78, rental income is still classed as income even if the mortgage is greater, only 75% of the mortgage interest - not the full mortgage payment - is allowable
OP, I can't imagine your bank would be happy with you not paying the full mortgage so you can pay unsecured debt, I agree it might be a good option for you but it's not for them.
Have you looked at other ways, perhaps getting a loan at a lower rate and obviously getting rid of the cards? We did that this year and although it felt like losing a security blanket initially having no CC, it's great as it forces us to keep on top of everything.
Still have the millstone of a rental property (former home failed to sell) around our necks but it gives a little boost every time I think at least there's no CC bill arriving!