ONS - the rate of annual inflation was driven by lower electricity and gas bills, as well as cheaper food costs.
RPI was driven down by the same factors, as well as lower mortgage interest payments and home insurance.
While the CPI is important as the rate that is targeted by the B of E in setting interest rates, the RPI is used by many companies as the starting point for wage bargaining.
The key difference is that the RPI measure includes mortgage costs, which have dropped significantly as the Bank has cut interest rates over the past year.
The official CPI figure is still above the government's target of 2%, but the Bank expects it to fall further during this year.