Interest rates, inflation, and jobs

Inflation is a trend rise in prices over a period of time, and also the decline in the value of money over the same period of time.  This link explains more.  It is impossible to calculate the rate of inflation exactly, as we have to make assumptions which are not necessarily correct.

Suppose for example that your weekly shop includes a Mr Kipling battenberg cake.  When the price of a Mr Kipling battenberg cake rises, then so too does the cost of your weekly shop - or not.  For one thing, the increased price of the Mr Kipling battenberg cake might be offset by a fall in the price of other goods that you buy.  Even if other prices do not fall, then the overall cost of your weekly shop will increase only if you continue to buy the Mr Kipling battenberg cake.  However you might react to the price rise by buying the store-brand battenberg cake instead - in which case the overall cost of your weekly shop might fall.

The BBC is reporting today that inflation has exceeded the target of two percent. It states that:

The Bank targets CPI inflation of 2%, but is currently holding off raising interest rates to control inflation because the unemployment rate is too high.

It is generally held that raising the Bank of England's base lending rate tends to put downward pressure on inflation.  I won't argue with that right now.  What I am wondering is whether or not the Bank is right to assume - as it appears to do - that an increase in interest rates would either cause unemployment to rise or at least not to fall very much.

My first comment is that unemployment is barely falling at all at the moment - just 24,000 in the last quarter.  My second comment is that there is - so far as I am aware - absolutely no evidence that interest rate adjustments necessarily impact upon the level of unemployment.  I have looked for such evidence, but cannot find it.

If anyone can supply such evidence I would be grateful.  I would be interested in statistical evidence of a correlation in a particular country over a significant period of time - not just one year.  I would also be interested in robust economic reasoning.  I have heard enough platitudes from bad economists, and do not wish to hear any more.