This is a question which I have been asked many times. It does not matter when you go to Florida, as you can enjoy the best weather at any time of year. If you are planning on taking your family with you on your trip, then February and March are the months that provide the best climate for families who want to take advantage of all that Florida has to offer during their vacation. The majority of resorts in Florida open up again in July and August for those who wish to visit during this period so it would be worth checking these dates out if possible before booking your holiday accommodation.
If this will be your first time visiting the area or if it will be some years since you last visited, then I suggest looking online for good deals where some companies offer packages which include flights from London Heathrow Airport along with hotel accommodation (and possibly other extras) – prices may vary depending upon how far away from Orlando/Miami they are located but generally speaking prices start around £350/$700 per person (single occupancy).