The structure only works if the saving is deliberately kept on the loan. We model it with your total monthly outgoings held where they are today, so the money the consolidation frees up goes onto the mortgage instead of being handed back as a lower minimum.
That's the difference between stretching debt out and clearing it sooner — and it's why the accounts being closed behind you is part of the plan, not an afterthought.
General information only. Whether any of this suits you depends on your circumstances, your equity and lender policy, and it needs to be modelled on your actual numbers.