Some times predicting is easy. You look at what happened when somewhere else tried something, and reckon the same will happen when your country does. With QE that may not be so easy. Japan has been trying QE for a long time. In their case inflation stays very low, output does not expand as quickly as they would like, so they just do some more. Japan has become the most heavily indebted of the advanced countries, as successive fiscal and monetary stimuli fail to inject inflation or supercharged growth into the economy. The government has racked up record levels of debt.
The high debt levels are less worrying than they seem for two reasons. The first is a lot of the debt the state owes to itself. Once issued, the Bank of Japan buy the debts back for the state with created money. The second mitigation is the interest rates on the debt remain tiny, thanks to QE purchases of bonds designed to keep rates ultra low.
I suspect the US and UK are different from Japan. Both the US and UK economies are now growing more rapidly. There are signs of monetary growth without QE. Both economies have a past history of being prone to more inflation. The USA keeps talking about getting interest rates back to a more normal level.The UK has deferred any such plan, thanks to the collapse of commodity prices and the greater strength in sterling, limiting inflation for the time being.
The Fed and the Bank of England are rightly wary of moving too fast to raise rates and choking off recovery. They are also conscious that for the time being they are more likely to undershoot their inflation target and have to explain why, than to face an inflationary issue. The US recovery is more advanced and has been proceeding for longer than the UK one. The US commercial banks are now generating extra credit, and US money supply is now growing at 8% per annum. That should be pushing the Fed to earlier action on rates. It begins to feel as if the economy and the banks in the USA are more normal. 0.25% as a base rate is anything but normal. The UK will have the luxury of watching what happens when the USA does start to make her move to normalise. If, however, the UK had a change of government policy to increase spending and borrowing, the UK might find markets intervened and started to drive sterling lower which in turn would start to increase prices.