Inflation, and the Bank of England (BoE) base rate are not the same thing. However, the BoE may use, and do use, the base rate to influence inflation.
The base rate is the measure that the Bank uses to calculate how much they charge to lend money to other financial institutions. This then impacts the interest rate that these institutions charge the public and businesses to borrow from them.
For example, if inflation is particularly high, then the BoE may increase the base rate, which will filter down to the public in the form of higher interest rates on any borrowing. This will then slow down public spending, as the public are paying more for their debt, and therefore have less money to spend elsewhere.
If inflation is very low, or negative (deflation), then the BoE may lower the base rate. This would mean that financial institutions can borrow money from the Bank at lower rates, and therefore should be able to lend the public money at lower rates. With the general public spending less on debt, they will have more money to spend on other things, and inflation will rise.
Currently, inflation is very low, but the base rate is also at historic low levels, so the Bank has less room for movement. Additionally, the mortgage sector often sees the biggest result in lowered interest rates. Most of the public’s debt is in mortgage form, and as certain areas in the country are seeing a small house price boom, lowered base rates would further drive that.