We are travelling from Manchester UK to Miami via Atlanta in March to connect with a cruise. Our flights have been booked by Princess cruises. They are insistent that a layover time of 1hour 25 mins is sufficient to pass through security etc and connect with our delta flight to Miami. Will we make it ! Also who is responsible for getting us to Miami in time to board our cruise ship?
I'm assuming this is a single ticket. Two separate tickets are a clear non-starter here.
They are insistent that a layover time of 1hour 25 mins is sufficient
Delta's minimum connection time in Atlanta for international to domestic is 85 minutes, so it's right on the edge of a legal connection.
Since Atlanta is your first point of entry in the US you need to go through immigration, collect your bags, go through customs, drop your bags again after customs, go to your departure terminal, go through security, go to your gate.
If everything operates normally, this is doable but there isn't a whole lot of room for error (delayed first leg, long lines at immigration, lost bag, long line at security, etc.)
Will we make it?
No one knows for sure. I think you have a good chance of making it, but there is also a non-trivial chance that you won't. A lot depends on your specific details. Things that speed up a connection are: flying business, status with the airlines, Global Entry, TSA PreCheck, no checked luggage, etc)
Also who is responsible for getting us to Miami
The airline is. If you miss the connection (through no fault of your own), they will put you on the next available flight to Miami. Delta has 8 non-stops a day Atlanta to Miami.
in time to board our cruise ship?
That's a tricky one. The airline has the obligation to get you to Miami, but they can't guarantee a specific time. Since the cruise company booked the ticket, they probably have some process to deal with delays. This may include flying to the first stop after Miami, if you can't get to Miami on time or expediting your pick up from the airport.
I would look at the Delta ATL-<MIA schedule for that day and check with ones would get you there on time. If there are one or two later flights that would work as well, then there is no harm in staying with the short connection. If all goes well you make it and have more time in Miami. If you don't, you just take the next flight.
If the short connection is the only option that still makes the cruise, I would call the cruise company and ask what happens if you miss it.