If I understand correctly, under the dominant system of fractional reserve banking, many (all?) private banks can create money by lending. See, for example, Implications of abolishing Fractional Reserve Banking on mortgages and interest rates. So, money created when people (or other entities) go in debt, and destroyed when those debts are paid back.
History has shown that when banks have the power to create money, they create too much in the good times, causing financial crises, and then create too little money in the bad times, making recessions and unemployment even worse. They put most of the money that they create into house price bubbles and speculation on financial markets, and only put a small amount into businesses outside the financial sector. We simply don’t think that banks, with all their incentives and need to maximise their profits, can be trusted with something as powerful as the ability to create money. And it’s not enough to regulate them, because regulators have already failed to keep them under control, and there’s no reason why they should get it right this time around. We need to stop banks being able to create money. Instead, we want to see the power to create money transferred to a democratic, accountable and transparent process (...)
What would be the consequence if only a single institution, accountable to the national government, had the ability to create money? Assume that this institution would use a more or less objective set of criteria to determine how much money to create, for example, in order to meet particular targets.
Edit: A commenter requested more background motivation why this question is specifically about banks. Allegedly, the system leads to increasing house prices and debts, along with other problems. My question here is not whether the issues that Positive Money are correct in attributing those problems the current system of private banks creating money; regardless of their correctness, my question is, as stated above, what the consequences would be of having only a single government-controlled institute create money.