The Bank of England is the only entity allowed to create or destroy our currency. It uses this power to lend money or accept deposits at a defined interest rate with the aim of controlling the economy's growth and inflation. Not everyone can borrow from or deposit money at the Bank; it only lends to other banks or building societies, and even then only over a few fixed (and usually very short) periods. If a bank wants to borrow or deposit money for a different length of time, or needs more flexibility on how much and when they borrow or lend, they have to go to another bank. However, the rates the banks lend money to each other (indicated by LIBOR) are higher than the Bank of England's rate as other banks can't produce money and so may not be able to pay back what they borrow. Banks make a profit by loaning money to other companies (including other banks unable to borrow money from the Bank of England) at rates higher than LIBOR and credit their deposits at lower rates.
But what if Britain had no central bank? If no one could create money and there were no (effective) money controls then Britain's net imports may eventually lead to a shortage of pounds; people would be forced to use another currency for day-to-day business. However, if the money controls were too tight exports would be hurt, as international investors would find it hard to get the money needed to buy British goods. We would therefore need a way of creating new money. With no central bank, and therefore no variable monetary policy, the value of a pound would have to be fixed relative to either another currency or one or more goods. As the government (or an independent institution) could only provide new notes when the appropriate deposits were placed with it, inflation would only depend on the changes in value of the deposits.
In an economic downturn, credit would be harder to come by as there would no longer be an infinite supply. Banks would still loan money as they need income, but they would be far more selective in who they loaned to. Demand for credit would quickly outstrip supply, bankrupting unprofitable companies and halting unsustainable lifestyles - but this reduction in private and public debt will speed the return to growth.
Unlimited sources of cheap credit have fuelled many asset price booms. Without the Bank of England, the amount of money a commercial bank could lend is limited by its deposits. During a boom speculators withdraw their deposits and take out loans to invest in the booming assets, and so the laws of supply and demand will limit its extent by driving up the cost of credit.