By Mollie Quirk According to sources, King Charles DID in fact offer Prince Harry a place to stay when he came back to England last week, but the Duke “turned it down”. Last Tuesday, Harry touched down in London after flying back to the United Kingdom from California. The Duke of Sussex came back to his former country of residence for the 10th anniversary of the Invictus Games, with him attending a service at St Paul’s Cathedral on Wednesday. The Duke of Sussex is reported to have stayed in a hotel on his brief UK visit, which came after he and his wife Meghan Markle handed back the keys to Fr…