Somewhat indirectly they would have limits, they're called "reserves" and it's the amount of funds the bank must retain and it's a percentage of the amount of deposits they have on hand. Each country is going to be different, but 10% is probably pretty standard in normal times.

So if a bank has £100 in deposits, and had 10% reserve requirements, they could loan out £90 and just hold the remaining £10 and would have no more money to loan out.

What get's crazy to think about is that when they make this loan, it's very possible that this amount get's deposited into another bank. Meaning another bank has £90 (with a 10% reserve) and they can loan out £81 and start the cycle again.

In that scenario there is only £100, but person A has £100 (which was the deposit) person B has £90 (that they owe back to the bank) and person c has £81 (that they owe back to a second bank) for a total of £271 of owned money, when there's really only £100.