I am a bit confused about the distinction between regular and normal - they both seem to share the meaning of conforming to a standard or governed by one. Royal Mail for example talk about normal delivery - could that not be regular delivery (can't imagine an 'abnormal' delivery)?

The words mean about the same, but are used in different contexts. For the mail, normal would be the base service, nothing extra..
Normal delivery is contrasted with "special delivery". In the US, the postal service has normal delivery, registered mail, special delivery, certified mail, etc.
Regular delivery would be the delivery that happens on a regular schedule and the same route (the same every day, 5 or 6 days per week).
Good Point George. A regular happening is a timely coinsurance. A normal happening is something that happens as it is supposed to.