Carnival have done a superb job in remaking UK▸ passenger shipping. Cruise ships even call at Liverpool.
I agree to a point - I've sailed with P&O and will be again at the end of the month (on their new, biggest ship, Britannia) and last time the "British-ness" of the P&O Brand and quality of on-board service was undeniable. Though I've not experienced them, I expect that Holland-America still "feels" Dutch and Costa still "feels" Italian, although they are also part of the same Corporation (along with Princess Cruises).
However, look beneath the surface and it is possible to detect that there is a Corporation in control - the ships are registered in Bermuda, which I expect has all sorts of "advantages" in terms of tax and employment law liabilities. The ships (the big ones built in recent years, in any case) have nearly all been built in the same Italian shipyard (Fincantieri) and are all probably quite similar under the skin, which of course makes them cheaper to build, as larger Contracts can be negotiated. You get the idea.
Nevertheless, this is the way of The World and if it must be this way I'm glad that the owning Corporation allows sufficient autonomy within the brands to provide a service that appeals to the markets they are looking to serve.