There are usually loads of disabled spaces free and rarely enough P&C spaces, so I put that you are BU. If you have a blue badge, park in the disabled zone.
Less than 5% of the population have blue badges, equivalent to the 6% of parking spaces available; 26% of households have a child under 12 - far more than the 5% minimum (but up to 10%) of spaces allocated for parents with children.
So no, blue badge holders should use the disabled spaces and leave the P&Cs for Ps with Cs. [We have a blue badge for a family member. I would never use it to park in the P&C zone.]