Interest rates are effectively the 'rental' cost of money.
When money is borrowed, the lender charges a percentage of the amount borrowed for each year the money is loaned out. When money is deposited in a savings account it is the bank that pays the consumer a percentage of the money for the period it is deposited.
Banks and other lenders set the rate of interest they charge/pay out on the Bank of England's base rate. The base rate, the underlying cost of borrowing in the UK, is set by the Bank of England's Monetary Policy Committee (MPC) – which meets on the first Thursday of every month.