Even with a Commercial Airmans Certificate (aka CPL), you would also need a Air Operators Certificate before you can advertise services to the general public. This helps ensure the operator has procedures in place.

IANAL but because "funds" change hands and involves people with no prior relationship, its commercial enough to be a problem.

Organizations such as Angelflight do facilitate volunteer pilots flying people around for charitable purposes such as transport for medical care. This is legal as the pilot doesn't receive any compensation for the flight.