7:54 AM PT -- King Charles just emerged from his meeting with Prince Harry at Clarence House -- one that only lasted about 45 minutes or so -- and His Royal Highness was all smiles next to Camilla.

This is one of the first times we're seeing the King since word of his cancer diagnosis broke -- and he's surprisingly in very good spirits. Now, he's on his way to Buckingham Palace.

Prince Harry has wasted no time hopping on a plane to London to see his dad less than 24 hours after Buckingham Palace announced King Charles has cancer.

Harry flew private from LAX to London's Heathrow Airport and arrived at 12:20 PM London time. He beelined it for Clarence House ... where his father is staying.

It's unclear how to read this ... whether Harry's quick move in any way intersects with the severity of King Charles's diagnosis.

As you know, Harry and his dad have a fractured relationship, although it's more cordial than Harry's relations with his brother, Prince William.

As we reported, doctors discovered the cancer during a procedure for an enlarged prostate. It is not prostate cancer -- though, the Palace was not more specific.

It's unclear how long Harry will stay. We also don't know if there are plans for Harry and William to see each other, but it would seem that would be hard to avoid given that William is probably spending time at Clarence House as well.

BTW ... Meghan Markle did not travel with Harry.