In our opinion, both of the main London airports (Heathrow and Gatwick) are equally good. If you are attending the Pre-Cruise Extravaganza, both have easy options for getting in to the city via train, tube, or taxi. If you are only coming on the cruise, you’ll find bus transfers to Southampton from Heathrow and bus or train transfers from Gatwick.
General information about transfers can be found here:
Heathrow to London: https://www.londontoolkit.com/travel/heathrow_central_london.htm
Gatwick to London: https://www.londontoolkit.com/travel/gatwick_transport.htm
Heathrow to Southampton: https://www.londontoolkit.com/travel/heathrow_southampton.htm
Gatwick to Southampton: https://www.londontoolkit.com/travel/gatwick_southampton.htm