Unless your children are very young I do not think you will go far wrong with Royal Caribbean, Celebrity or Princess for children's activities, professional staff and price. It would probably be best if you decided whether you would like the hassle or excitement of flying to your departure port or sailing directly out of the U.K., as there are, when you consider it, many points for and against such as having more time in the Med. area and suffer British airports with children in tow or sailing through Biscay but allowing the children more time to enjoy the activities on board....Hope that helps....Leanne Dow.
Princess and P&O, all P&O ships apart from Arcadia and Artemis and all Princess ships sailing from the UK.
Royal Caribbean is considered to be the best for children's activities. The brand new Independence is sailing out of Southampton from May 17th.
One possibility (although not to the Med) is P&O Aurora cruise to the Canaries and Madeira, which sails from Southampton on 21st June for 9 nights - I know because we are booked on it. Graham.
I would recommend Princess Cruises and its ship Sea Princess as its very family orientated and has lots for kids of all ages even us older ones :) the best part is it sails in and out of Southampton so no need for the airport makes for a much better holiday..hope this help.