A Claims Management Company (CMC) is a wholly unnecessary middleman which sends leads to law firms. Before April 2013 CMCs used to be able to sell claims to Solicitors. After April 2013 it became illegal to sell a personal injury claim and therefore the CMCs today sell batches of leads, not claims. A CMC is regulated by the Ministry of Justice and not the Solicitors Regulation Authority (SRA).
If you have suffered a personal injury and require legal representation go straight to a solicitor who specialises in personal injury law and not to a CMC.
CMCs tend to be better at marketing than law firms and that is why they have existed.