The equilibrium price and quantity for a good or service are determined (in a free market) by supply and demand. When supply or demand changes, the equilibrium price and quantity will change as well. In the scenario you present here, the change in the price of fuel will lower supply while the change in where consumers want to go will lower demand. In both cases, the equilibrium quantity will fall. In Scenario I, the price will rise while in Scenario II it will fall.
One thing that can change the supply of a good or service is a change in the cost of making it. When the price of fuel rises, it becomes more expensive to “make” flights to London. An increase in the price of providing the flights will lead to a decrease in the supply of those flights. This is shown on a graph by a movement of the supply curve to the left. This results in a new equilibrium in which the price is higher and the quantity is lower. In other words, there will be fewer flights to London and they will cost more to buy.
One thing that can change the demand for a good or service is consumer tastes. If people come to prefer going to Italy, there will be less demand for going to London. When this happens, the demand for flights to London decreases. A decrease in demand is shown on a graph by a downward (and to the left) movement of the demand curve (in the link below, there is a graph showing changes in both supply and demand). This results in a new equilibrium in which there are fewer flights to London and they cost less to buy.