All are very good but be each company varies depending on ships and itineraries. P&O for example, caters for different styles of cruisers - the Artemis being the older, more traditional cruising, while ships like Oceana and geared more at families. For a traditional British cruise on a good ship, I would recommend Queen Mary 2 - For a slightly younger feel - and child free - you could book Arcadia. Best thing is to speak to a cruise consultant, as without really knowing your parents it's hard to sa.
You should look at Fred Olsen, they pride themselves on being British, The ships are slightly smaller, which may help aged walkers etc, remember not to go in school hols as you can avoid some children.
Take a look at Spirit of Adventure if you think they'd enjoy a relaxed, friendly, probably no-children ship that's small enough to go right into ports (few anchor ports) and caters more for active middle or senior ages. Also, shore excursions at every port, and gratuities, are included in the price (with some extra optional excursions available if wished) so your parents wouldn't have to fork out the extras for these. As a previous post has said, it depends on whether or not your parents would enjoy a glitzy all-singing/dancing ship or one with some culture, good dining options, brilliant library/internet and small enough to get to know quickly.
Elizabeth, Bury, Lancs.
I would recommend MSC (meditteranean Shipping Company). Their ships are immaculate, service excellent and some great itineraries.
MSC and Costa are Italian Cruise Lines and naturally have majority of Italian cruisers who tend to go in large family groups with lots of children. My recommendation for typically English, older cruisers would be P&O Oriana or Aurora. Different ships within the same cruise line have a different atmosphere and also are different according to time of year. All are much livelier in school holidays.
Choose P.& O. every time! The Fred Olson ships are very small, and if it is at all choppy they may be sea-sick! Far better on say the OCEANA, which has wonderful stabalizers to combat any rough seas.
Also possibly choose a Caribbean cruise, as again the water there is always very smooth. Fly there and back is best, then you have seven or fourteen days visiting a different Island everyday. Absolute Heaven!!!