Inflation up = need to raise interest rates to cool the economy down
Interest rates up = GBP more in demand compared to other currencies (ie switch into GBP and earn the new, higher, GBP interest rate)
It's not always obvious... However, in general, structurally lower inflation would probably imply a stronger ccy, all else being equal. If, on the other hand, there's an expectation of the fall in inflation being short lived and temporary, it's likely to imply a weaker ccy.
In the UK, we would probably have a really hard time imagining that we could have inflation running low for a long time. So we assume the opposite, which means that lower inflation currently translates to a weaker sterling.
Need to consider 'real' rate of interest compared to nominal is important! (r - i = real r)
Google & read up on the JPY USD carry trades if you are interested to find out more. Bear in mind exchange rate movements too in determining flows and real gains.
Another example; this is why it makes sense for foreigners to buy UK assets at the moment. UK looks like it may have to raise interest rates before Europe does, if inflation and employment likely to start rising before Europe. Thus, a European investor who borrows at cheaper %r will also benefit from positive currency movement when they sell UK asset and convert monies back to Euro or lose out if Euro appreciates faster than Sterling based on real interest rates etc.
Ideally one needs to consider all three variables in determining net effect on currency.
If you are only interested in inflation then as Martin points out "all else being equal" you would need to consider inflation between UK and Eurozone to compare net effect on currency pair.
Falling inflation is normally bad for a nation’s currency as you’d expect the central bank to reduce interest rates to stimulate the economy and get inflation back up,
such as happened with the ECB and the Euro recently. This would normally lead to the country paying less interest on its debt, making it less attractive to the markets, and thus requiring less demand for the currency in order to buy that debt. It usually depends on where inflation is in relation to the central bank’s target (ECB/Fed/BoE= 2%), however, due to the financial crisis, other factors like unemployment and financial stability have become more of an issue and so some are allowing more /less inflation whatever the weather. I hope this helps.