DH has the same name, First and Surname, as his father, but with a slightly different spelling. (Eg. Matthew / Mathew)
His father has multiple CCJ's against his name, but they are also showing up on DH's credit file. Is there any way we can have them removed as they are not our debt? We've spoken to the company who ran the credit check who said they could dispute it, but they're now saying they can't. We are at the end of our tether as it's causing a problem with our credit ratings.
It sounds like they have contacted the organisation(s) that got the CCJ against your DH's father and they have refused permission to amend the entry. Your next step is to contact the lenders and insist that they permit this information to be corrected. If that fails you can report the matter to the ICO (Information Commissioner's Office).