In the main though its for goods beyond the control of the UK government.
OPEC are advising their members to restrict production, which is elevating the price of oil, which in turn affects road fuel (which affects the price of evrrything), plastics, fertilisers, etc.
Building materials are in short supply due to weather conditions in Scandiavia (wood) and America (polymers and concrete ) so prices are going up there.
And on it goes...
So while inflation is rising it is due, in the main, due to things beyond the control of the UK. That being the case, further screwing headline interest rates upwards won't have any real effect on rising prices, as they are due to factors external to the UK economy - its not runaway consumerism leading to these rising prices.
I don't think there is much cheer yet for savers, but there is also not much prospect of a late 80's inflationary scenario, never mind a Zimbabwe one.