Can a royal mail can run a red light

I think there may be a bit of confusion here!

A "Royal Mail van" is a vehicle used by the Royal Mail, a postal service in the United Kingdom, to deliver mail and packages. It is a vehicle, not a living being, so it cannot "run" a red light or make any decisions for that matter.

In the UK, it is illegal for any vehicle, including a Royal Mail van, to run a red light. The driver of the vehicle is responsible for obeying traffic laws and regulations, including stopping at red lights.

So, to answer your question, no, a Royal Mail van (or any vehicle) cannot "run" a red light.