How can i stop nuisance calls?

i am in the UK and i have been receiving calls from a company called Fresh start Finance since last year, every time they call me i tell them im not interested and to take me of their database, they say they would, but then a day or two i get another call from them, i tell them the same again. then i don't here from them for a few weeks, then they start again, and they use different numbers and even with held numbers. im getting really fed up now with it all, they call on my mobile, i started to ignore them and put numbers to reject list but they phoning the land line, as i with my mum she getting fed up to, she keeps telling them that i have told them to stop calling but they take no notice, even ringing and hanging up when we answer home phone, my mum is ill and she don't want this harassment and phone calls, i want to register with the TPS to stop it but worried, by registering number do calls get blocked from calling, the reason for asking this we got family/friends who's numbers are automatically with held. so would we still receive calls from them or would registering block these coming through. if anyone can help i be grateful as this is getting beyond a joke now, why don't they just take no for an answer, not good. this needs to stop.