You could argue that by keeping the base rate at 0.5%, the government/BOE are doing everything
within their power to keep the cost of living down.
Traditionally, when inflation starts climbing, the base rate is raised to combat it. This increases the cost of borrowing (impacting mortgage repayments and car repayments for the average man in the street) and generally reins in people's spending. By forcing a tightening of belts across the board, inflation starts to come down again. It's all a balancing act (when it works).
However, inflation is above target quarter on quarter at present, because of external stimulus (commodity prices, devalued currency etc), not because UK people feel flush and are all splashing out on new tellies and foreign holidays. The external levers are in no way affected by the raising of the base rate - so the normal BOE response would only makes things worse. Fuel and groceries still go up, but people's mortgages also cost more. A world of pain, followed by a load of folk defaulting on mortgages. Not the first time it has happened.
So what are the alternatives? The government can only raise public sector salaries if they want to continue Labour's f'up spending policies. If the world markets think the UK are splashing the cash again, the markets will further devalue the pound in response - which leads to higher inflation, and the whole merry-go round continues. The private sector are free to do what they like of course, but most companies are not looking for additional overhead in the current climate...
They could cut taxes to help the man in the street but that would further aggravate the spending cuts (or it would increase the tax take depending on your school of thought

).
At present, it is all balanced on a knife edge and a lot of people just need to hold their breathe and hope it all improves of its own accord. Of course that took over ten years in Japan and they are still struggling economically.