Because of the risk that swelling inside a cast can affect the circulation, many airlines restrict flying during the first 24 or 48 hours after a cast has been fitted. If you need to fly before then, the airline will usually require the cast to be split along its full length before you fly, as any swelling will not then affect the circulation. This can be arranged at the hospital. You may also have to make arrangements to have the cast replaced once you reach your destination. It is helpful to carry a letter confirming the date and time of application of the cast, especially if you have not had the cast split. Speak with your airline ahead of flying.
If you have a broken arm or leg, you may not be able to sit in an emergency exit row, because you may need to move quickly if there’s an emergency. Also, if you have a broken leg and are unable to bend your knee to sit normally, you may be required to purchase additional seats so that you have enough space. This will also allow you to elevate the leg during flight and will reduce any swelling that would occur if you kept the leg down. More information is available from UK CAA and NHS.