Quantitative easing was supposed to flood the market with liquidity, bring interest rates down and revive the economy. After the massive cuts in the MPC's bank rate, quantitative easing was the next step in the strategy to save the UK economy from deflation.
Once the Bank of England began buying government paper, rates did come down fractionally. However, they began to creep back up almost immediately. As of May 6, rates on goverment debt are higher than they were at the beginning of the year. So much for QE for reducing rates and reviving the economy.
The Bank of England and the government think that the bond market comprises of a bunch of backward looking morons. However, investors are forward looking creatures, and when it comes to UK fiscal and monetary policy, they do not like what they see. If bond investors are going to hold UK government debt, they will need to be adequately rewarded. That means higher rates on UK gilts.