I think that they are allowed to do this, yes. There have been recent court cases where people have complained about being forced into voluntary work by the authorities but they can do whatever they like it seems! I feel that your only option is to deny yourself benefit and turn down the job or take the job and at least be doing something and earning some money. If you turn down the job, you could consider becoming self-employed as an alternative to looking for paid employment.
You do not say where you have been looking for jobs apart from the job centre but I would advise you to look at agencies as well. Post your CV on the big recruitment sites and go to agencies in your local town. You may be able to find some better paid temporary work which will at least help ends meet even if they do not give you the work experience you are looking for. Plus they will look better on your CV than being unemployed.