Tax rises are a fairer way to go.
At the moment, only about a third of homeowners have mortgages, with about a third of them on tracker/variable rates.
So the interest rate rises are disproportionately targeting a small minority of people in the UK.
Tax rises to remove demand from the economy target all people with more than a certain income.
Saying all that, we don't need to remove demand from the economy as higher fuel prices and accompanying rises in everyday food and other items is doing that on its own.
But the most important factor behind the inflation is energy cost spikes.
That in itself should filter through the system over 12 months, but the residual price increases as suppliers of general goods and services add their increased overheads to their selling prices, will continue to rumble for another 12-18 months (but have a lower impact on inflation)
I doubt the BoE and ECB would be raising rates so much so quickly if there Fed weren't, though. They have more acceptance that raising interest rates in isolation in these current circumstances is not going to remove the inflationary driver (global fuel costs), whereas the Fed are tunnel-visioned on the matter.
Can imagine that next month, when higher interest rates have done cock-all to reduce inflation in the US, the Fed will conclude "Well that last interest rate rise didn't lower inflation, what shall we do now? I know! We'll raise interest rates! That'll lower inflation!"