I can't say I'm surprised to hear of a firm offering unpaid paralegal work, but I haven't heard of it first hand before.
What sort of uni are you at/degree are you on track for? If you're at a semi-decent uni and are expecting a 2.1, I personally wouldn't stoop to that level of work, because you're simply worth more than that.
I know it's tempting to clutch at straws when you probably have nothing vocational on your CV, but if you can get yourself on some vac schemes or even presentation days at firms in the next 6-12 months, then you'll be in good shape for future applications.
If it was one day/afternoon every fornight you were being offered, that would be different, but a full time job without pay is taking the mickey/illegal.