If you have a blue badge, best to avoid private car parks. You can park on the limited waiting spaces normally limited to 30 minutes, all day. Double yellow lines, 3 hours but not on corners etc. It requires a bit of common sense that you dont obstruct too much.
I recently wrote a letter on behalf of a neighbours claim. Poor man has very sore feet and is about 75. I see him trying to walk his dog and he does struggle.