The mechanism by which interest rate rises dampen inflation is through cutting household demand. Most households have debts: mortgages, credit cards, loans; or they wish to borrow to fund future purchases. As repayment costs increase less money is available for household purchases while some future loans become too expensive and so are never applied for.
In any event, demand is decreased and suppliers end up with excess stocks. They have to reduce their prices to the new market-clearing level (taking a hit on their profit margins in the short term) and price-inflation is thereby reduced.
According to BBC's Newsnight a few days ago, of the current 4% inflation rate around 2% is UK domestic while the rest reflects the VAT increase (which will drop out in a year), rising world commodity prices and rising imports prices due to the weak pound. The Bank of England could get inflation back to its target of 2% if it really wanted to, just by bearing down savagely on the domestic side of inflation (that significant interest rate rise again).
It won't though. An increased bank rate has other consequences: in particular it increases the cost of borrowing for companies, raising their internal project costs. This hits at their expansion plans and so delays recovery. There's also the downward pressure on profits already mentioned which also tends to drive away investment.
In short, the BoE should tough it out and wait until/if there are genuine signs of domestic inflation getting out of control. If their nerve holds, inflation should drop back to target within 12-18 months and we will still be best placed for recovery.
