Looking again at the possibility of using an alternative departure port to Southampton, I checked on whether Saga might have anything suitable for you out of Dover. They have - but one a hell of a price!
https://travel.saga.co.uk/cruises/ocean/where-we-go/european-cruises/lisbon-and-spains-atlantic-coast.aspx
I still think that the Ambassador cruise from Tilbury, that I linked to above, ought to be worth consideration. They're a new cruise line, only in their second year of operation. However they're based upon the old Cruise & Maritime Voyages, which had some of the best reviews among cruise companies. The Ambition is new to their fleet this year, having been completely refurbished to appeal to the company's over-50s target market. (Their only other ship is the Ambience, which came into service last year). Further, Tilbury is very easy to get to from most parts of the country
https://www.ambassadorcruiseline.com/before-you-sail/travelling-to-port/london-tilbury-port-information/
and their prices look much better than those of competitors like Saga!