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We have just returned from a cruise on the Royal Caribbean, Navigator of the Seas and we saw several(physically and mentally) disabled passengers and wheelchair users and one passenger using oxygen to assist his breathing. Their presence on board did not appear to be causing a problem for the other passengers or indeed the staff. It seems that Royal Caribbean do not discriminate against the disabled.
Have a look at these two cruises departing Southampton:
Arcadia 04.04.08 17 nights
Aurora 06.04.08 14 nights
I checked the P&O brochure and although it does state that you should advise them that you will require oxygen whilst on board, it does not appear to be a problem. Kind regard.
I would also try Celebrity Cruises,they are sister company of RCI Regards Iren.