Other points that you did not mention are that the previous government adopted policies that had the effect of moving people off the unemployment registers but not into useful employment. For example, raising the school leaving age and encouraging more people to go to University may have been useful social policies for some, but they also took people out of the unemployment data. Some of these people would probably rather be working, and might be better off doing so. And a large number of people who are officially on disability and sickness benefit (sorry - I don't know the numbers or the official titles for the benefits) could and should be working if there were suitable jobs and the welfare system did not leave them financially worse off by going back to work than staying on benefit. Unfortunately we have created a culture of learned helplessness for many, and done very little to encourage job creation in the private sector, which is where most of the wealth is created. The public sector, necessary though some of it is, simply takes money from the private and spreads it around, often inefficiently. It doesn't create much wealth itself.
The bottom line is that the real unemployment number is well north of three million and it is hard to see the private sector making much of a dent in it, at least in the short term and with jobs that don't involve stacking shelves or flipping hamburgers.