Well I doubt you are dumb, seeing as got on a Masters course and seem perfectly coherent in your messages. I think you are being too harsh on yourself. Despite the economic pick up the labour market is still saturated, especially at the graduate level, and getting a job is difficult. Don't feel too bad, you are not the only one in this situation. Get a recruitment agency to go over your CV, and get them to help you into employment. If that doesn't work I think you need to explore jobs and opportunities outside of where you are currently aiming, and start to remove the mental barrier of being too qualified to get these jobs.
If you get a CSCS card you can find Labouring work in construction. It is hard, you work in all weathers, but the money is often decent and if you put in the graft you'll find plenty of opportunities. Plus you can move on to other trades from there. A blue collar job working as a self-employed tradesmen is often better paying than your run of the mill office job.
The security industry is always looking for people, and although an SIA certificate will set you back a bit it will open quite a few avenues. The hours are often unsociable, but the pay is better than minimum wage. If you can handle dealing with drunks or spending your evenings alone in boredom guarding some sort of building it is a good job to do.
Bar work is another one to look at. Again unsociable hours and having to deal with drunks, but they tend to have high staff turnover so roles are usually open quite often. The pay is usually poor, but it is still better than nothing.
And as others have said retail. They often employ graduates and students, and the pay within the industry is currently on the rise. Can be mind-numbing work, but it pays the bills and is a good thing to keep you going. Also opportunities to progress within the corporate structure are usually good, at least in theory, provided you are competent.
Despite having a 2:1 I didn't fair well in the graduate field so decided to venture out. I have worked in most of the above fields, and they really aren't that bad, as well as being quite accessible to most people. At the end of the day a job is a job, and if it means having to stack shelves or shovel gravel it is better than being stuck on the dole. Nothing to stop you working on starting a career while in employment.