@opshelper well yes: firstly parking is not stopping, so you can argue you were stationary for an amount of time that was purely nominal. Stopping on a pavement is not a contravention, only parking is.
Secondly there is an exemption under 15(3)(b) of the Greater London Council (General Powers) Act 1974 "
for the purpose of saving life or extinguishing a fire or meeting any other emergency", but you bear the burden of proving that there was an emergency. What caused your family member to feel unwell and what symptoms did they have?