Getting to London International Cruise Terminal from Doubletree Hotel in London.

Slightly complicated journey, as the terminal is in Tilbury, far to the east of London proper. The easiest would be an Uber from the hotel straight to the terminal, but it’s a long, long way with heavy traffic and would take a long time and probably cost a lot. You could also take a taxi/Uber to Fenchurch Street Station and then a C2C train to Tilbury Town station, and then a Minicab from outside the station to the terminal which is close by. You could also take public transport all the way, but with luggage, I wouldn’t.

If you go onto Google Maps and search for terminal, you’ll see what the journey consists of.

Apologies if you've already considered and ruled this out, but I always find that just buying the cruise's transfer to ship is the way to go. It's a hassle free way to start your cruise.

If that's the one by Victoria Station, then I would take the tube (District Line) from Victoria to West Ham. Then a C2C train from West Ham to Tilbury Town station. Board at the very rear of the District line for easy interchange tap out at West Ham, using the lift/elevator.
The actual interchange is cross platform- so you could instead buy a London Underground Zone 1 (the Zone, not Victoria) to Tilbury Town through ticket, for £9.70 Off Peak Single to avoid the tap out/in at West Ham or Grays- then just do the cross platform West Ham change.

Alternatively tube to Tower Hill, walk up the street, use the side entrance to Fenchurch Street station for the same train, but I believe West Ham is the easier interchange, from long experience.
The bus #99 (not Sunday) runs every 30 minutes to the port. It is free to any rail ticket holder (as it is a permanent rail replacement for the liner trains which used to run to the docks).
It stops outside the Southend bound platform (where you arrive), goes to the Asda supermarket, then stops outside the London bound platform on the way to the LICT.

The way I do it is to Oyster/contactless to West Ham, tap out, then a C2C paper ticket from West Ham to Tilbury Town.

But Grays (the station before Tilbury Town) is in TfL Zone 9 (although in Essex) so you can tap out at Grays, then a ticket to Tilbury Town (a bit more expensive, oddly than the West Ham Combo).

There is interesting history in the Check in Hall- the Empire Windrush arrived at the LICT from Jamaica in 1948, and Gunter Pluschow made the only successful WW1 German POW escape home using the Tilbury to Gravesend ferry in 1915, then the ferry to the neutral Netherlands.

If you have time do go round the corner to the World's End pub, and the Culloden memorial stone- Jacobite prisoners from the Battle of Culloden were held at Tilbury Fort and in prison ships on the River Thames. A number of whom died- it was a grisly tourist attraction at the time to sail from central London to Tilbury to see the prison ships.

Alternatively your cruise line may run buses from London Victoria Coach Station to the terminal- mine does, but I prefer to make my own way there in my own time.

Thanks for the quick responses! We would normally get the transfer with the cruise line but we’re heading there a few days before, and it is not included. Would be worthwhile checking I guess. We’re thinking the cab/train/cab route but looking for input from other travelers. Thanks again!
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It's abou 30 miles if you are staying at the Doubltree near Victoria.

The other option would be a car service that would pick you up at your hotel and drop you at the cruise terminal. Probably cheaper than a cab and you would know the price before booking.