It really depends on what you consider to be a good deal. They do offer some good rates at times.
But if you just want a transatlantic cruise and don't mind when you go, there are always some really good deals on the repositioning cruises. Talk to your agent and they'll be happy to help.
__________________ Travel Agent/Cruise Specialist w/13 yrs exp and 48 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!
I presume that you already have the Princess return dates, so are fairly tightly bound on the TransAt options by that.
It might be worth talking to an agent and asking that "as they are both part of the Carnival group, can they try for a special price". They will often do it for follow-on cruises on the same ship, so who knows they may be happy to help, especially with the current high availability on the ships.
Good luck & hope you have a great time.
Last Cruise: Royal Princess August 2015
Next: P&O Oriana October 2015
Then: Queen Victoria January 2016
A couple who are good friends of ours use Cunard to go to Europe and back.
This lady will not fly and they travel to Europe every year so they cruise to and from, mostly on Cunard.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Vision OTS 2-14-2015
Friends have mine have just booked to join me in the fall. They will disembark in Southampton and remain in England while I remain on board the QM2 for the Europe portion and then re-join me for the crossing back to NY. They like me hate transatlantic flights.
Sun Princess (2 times), Mississippi Queen, Dawn Princess, Coral Princess (2 times), Regal Princess, Grand Princess (2 times), Diamond Princess, Maasdam, QM2 (16 times)
We are sailing from New York (Brooklyn) to Southampton on the QM2 in late Sptember 2013. Reserved a Balcony cabin for the 7 day crossing for about $1250 each, about the same price as (if not cheaper than) Princess' 7 day cruises.
Cunard is never too costly to use for a Transatlantic crossing, NY to Soton.
Would you "be happy in the lowest category cabin?" Why not? But you will not have a balcony. Inside cabin is entry price. You judge the worth.
If crossing dates work out for you, you arrive in Soton, take your Princess British Isles cruise, then take the back to NY crossing.
I just booked a crossing on 11/25 from NYC to Southampton just because I'm so over the flying thing and for the first time I'll be cruising solo.
I'll give you an idea of costs - my balcony stateroom cost $2300 including the 75% solo supplement and Cunard insurance, so for 2 people you are looking at something around $2,600 - you can go cheaper with an inside cabin, or more expensive with a Grand Duplex (I think they were $32,000 per person ).
Cunard offered me an absolutely amazing deal on the flight home (to Phoenix) - a business class seat on British Airways for $1,700 - which is about half BA's normal fare.
Personally I think $4,300 is a steal for 8 nights of cruising and a business class flight home after a week with the family - but it should at least give you an idea of cost.