If you are in Scotland, then probably need a ship going to Port of Tyne, some do Sheerness (Kent), Grimsby (Immingham, Humberside), and Tyne, but some ships do not also call at Tyne as volume there is lower. These ships can take thousands of cars so not going to schedule a ship to drop off just a few hundred cars.
Normally you then need to wait for a road transporter, which means need dealer to be receiving multiple cars. If you are long way from the Port it might be beyond a round trip within a days driving hours which means you need one of limited number of trucks where driver can rest. The general lack of cars means nowadays more likely to be waiting for other cars to fill the truck than awaiting for a spare truck.
In my experience most seem to leave port early hours and arrive at dealers from breakfast time onwards (presumably to miss traffic, and coincide with dealer opening hours).
But really your dealer should be able to work out which cars they are expecting are at a port or on a ship. There is another thread where a service Dept hasn’t got any available bookings for 5 weeks (I think it was Yeovil), but imagine having to wait 5 weeks for a PDI as wasn’t booked in as didn’t know when cars arriving.