If I were in your position, I would explain to my parents that I felt I was capable of attending an even more highly regarded university, and that I wanted to do them proud by excelling academically. Seeing as it's always safe to apply to one university that is slightly below your expected capabilities, I would include Cardiff on my application and have that as a safety net. Then you still have your other four spaces for Imperial, UCL, etc. I'm sure your parents will come round to the idea and be very proud.
... and the ones that won't