Does anyone have suggestions for safe, none prescription medication that my children could take to help them sleep on the flight from the UK. They both hate it. Thanks.
You might want to look into behavioural remedies. Thing with any type of drugging is that you can not turn it on and off as desired. Obviously odds aren't huge, but if something does happen with the flight causing an emergency landing and evac or god forbid worse; you do NOT want to be even the slightest altered. Let alone want kids to be, who will have a harder time in such situations anyways. More common risks? Again, it is not a switch that you control. Some folks react different to a same product in air versus on the ground. Then there are stuff that influence sleep cycles that come with a nasty habit of having to behave as the medication fits. For instance; take it at a moment and have the sleepiness hit at a moment where you are still active (boarding, eating, going to the bathroom) and you can easily no longer get the desired benefits but have it result in a negative thing feeling poor etc. And the list goes on.
I personally need a lot of extra medication on top of my daily norm when on a flight to the US to simply physically cope. Have never been a fan of the risk of drowsiness because of stated above, but after being on a flight where we were instructed about evac since there were some problems that could result in needing to do an evac right after landing and seeing how those that did use "aids" (including kids being given something as "harmless" as benadryl), I've decided for myself I've seen enough. Any and all meds that might cause me to be altered in any way or shape are not an option to be in my system during flight.
What can be done that does not alter the state one is if need be? Behavioural. Most of the UK flights will leave anywhere between morning and afternoon. Keep the kids up during the night before. Turn it into a party, breaking some smaller day-to-day rules to make it a "huge thing". Movies, active games during the most difficult hours, no foods or drinks that make them sleepy etc. You tend to go to the airport early enough anyway, so that should take at least some of the night away if not a big portion if on an early flight. For youngsters it can be harder to skip a whole night out of nowhere. Consider prolonging up their bedtime a couple of days before. Skips as small as 30 minutes per day going to bed later can result in them being able to hang on an hour or 2 more when needed. At the airport; active stuff, keep them alert. Not just great to blow of some last steam before a flight but again will keep them awake.
After boarding, the excitement of finally getting onboard, excitement of food -hey, still a kid- etc dies down, most will beyond craving to go to sleep after pulling an all nighter. For the younger kids; bring along their sleep routine. So; change into pyama, have their usual cuddly blanket or stuffed animal at hand, read the usual bedtime story. Routines are a great little helper for youngsters to get into allowing themselves to feel the sleep. Depending on flight time, you can even play with this to such an extend you come as close to Florida evening time before they go to sleep. Does not just get them to sleep during the flight, but also helps them combate the jetlag. If doing so; be aware that you will also want to beat the jetlag with having kids up and about.
Being Dutch, we have a 6 hour time difference with Florida. You already have one less to tackle, so to say.

Seriously though, that shifting in bedtime is key in our family that flies extensively. Most destinations have 6 hours difference (Florida, Thailand, Australia etc.) so we tend to start a week prior to departure by shifting. Night before the flight; no getting to bed. Works like a charm to have very little if any jetlag and sleep in flight. As soon as we hit the airport, we start living at the time of destination and prefer to plan sleep during at least evening time at destination. Flight back; where possible again slowly we begin to work in local time. Coming back from Florida, having a short night (get up around 5am) then keep on going until on the TA flight. Not only long enough to get some proper sleep but again; long enough since having slept to physically want to sleep and great timing to get back on home time again. Has a huge possitive effect on adapting to the new timing.