We love to combine cruises with a land trip.
In particular, we have done three transatlantic cruises in conjunction with a land trip ( two cruises west bound and one east bound). Also, we did a lengthy trip to Australia and New Zealand in 2018 and took a transpacific cruise back (Sydney to Seattle).
Transatlantic and trans pacific cruises are cheaper per day than other cruises because they are "repositioning" cruises.
The key is to find reasonable air fare for the one-way trip.
Sometimes the cruise lines can offer a discounted fare. Also, we have used frequent flyer miles for the one way trip as well.
Further, we lived in Germany for four years and have much experience with land travel, via auto rental, rail and bus tours.
Here are a few tips about your land travel.
I suggest that if you plan to do a land trip prior to the cruise home do at least 2 weeks or more.
We did a four week drive tour of S. Wales and England prior to our transatlantic home from Southampton in 2017. It was great.
Here is my detailed review of our trip:
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139
It would be wise to plan as little lengthy travel by air on your land trip. You mentioned flying into France, Portugal, Spain, or Switzerland prior to departing from Southampton. I suggest sticking the UK or perhaps France. Yes, you could do the other countries (not all on one trip unless you have a couple of months), but significant travel will be involved. If you have to fly within Europe, that will cancel out much time just dealing with airports, etc. Yes, discounted airfares many be good, but you usually can't take much luggage, etc.
Also, plan your trip ahead of time by what you want to see and transport between places. Don't plan on a rental car where you cross borders and have to pay a huge drop charge. Once you determine where you want to go if you have a lengthy rail trip, book it in advance. Just showing up at the train station, especially in Spain, Portugal and Italy can take a while to buy your tickets.
You can show your cruise booking to explain how you plan to leave the country (UK).
Different rules for different countries in Europe regarding COVID19. Some require either vaccination/booster no more than 270 day after. Others do not, be sure to check the country requirements. For some, if you aren't vaccinated, no problem, or you have to take a COVID test prior to getting on the airplane to get there.
Also, protect your valuables at all time. Especially in places like Rome, Barcelona, Madrid and Paris pickpockets are terrible. Wear a money belt. Also, carry a copy of your passport in case it is stolen.