We will be taking a cruise and need to go from Heathrow Airport to the terminal and then from the terminal to Gathwick Airport. Please advise.
Could you give a few more details on timings, number of passengers, mobility with luggage, budget? There are a number of different options based on these details.
This site give a good overview of the various options
https://www.londontoolkit.com/mnu/london_airports.htm#southampton
We used West Quay taxi, based in Southampton to get us from Gatwick to our hotel in Southampton. Contact them for a quote.
We have used International Friends on several occasions. They will give you a quote based on the time of day and type of transport that you provide. We used them from Central London train station to Southampton, Central London to Heathrow, an from Southampton back to London with a shared group. They are wonderful. https://www.internationalfriends.co.uk/
We were impressed with their professionalism, promptness,and price.