London to Milan is roughly 540 nautical miles and a little under two hours in the air. Every jet class can fly it non-stop, and it is one of the routes where a light jet makes the most sense: short enough that a larger cabin buys you very little.
Private jet charter from London to Milan starts from $10,000 on the smallest suitable aircraft. That is an indicative starting price, not a quote: the figure for your trip depends on which aircraft are available, where they are positioned and the date you fly.