I've taken that flight to Tampa before and it was pretty god - mostly because we left on a Wednesday and it was full of pensioners (and not even full at that) in mid May. Also, it gets you where you need to be if you are headed to Gulf beaches.
Note, however: BA has pulled the second meal in Economy in flights 8 hours or less and replaced it with an "ambient snack" (their words, not mine) which is a basket pass of either one biscuit or one fun size chocolate bar. Also, when I flew them to Chicago in August (at the start of this all), the outbound food from Heathrow was almost entirely carbs and I totally fritzed out ina massive sugar rush and then crash. I would highly recommend:
a) Bringing water for yourself and kids (they are cutting back on water runs; water in economy meals has been reduced to a "cuplet" rather than the previous bottle) - either buy at airport or bring empty bottle through security and find a fountain.
b) Bring healthy snacks in case its straight carbs on the plate
c) Possibly some sort of energy bar or crackers or something to replace the second meal for the kids - by the time we loaded the plane, pushed back, held at heathrow etc we were way past 8 hours flight time and I was STARVING by the time we landed in Chicago, the only food really being the small economy meal 6 or 7 hours before. And no, candy is not a substitute and just makes you feel worse, not to mention they did a very poor coffee/tea run at the same time
d) They've also cut peanuts/pretzels with the first drink run in economy. Do without or bring your own (I actually found I missed these strangely enough)
BA is starting to move over onto my personal Do Not Fly list (along with United, Spirit, and USAirways) because of a lot of these cuts and Im not a fan of their CEO and corporate strategy. However, sometimes they are the best time/route/price and for a destination like TPA, and you are prewarned about service cuts, you can deal with it to get to the beach!