The woman was reported missing as the ship sailed from Oporto to Barcelona, P&O Cruises said.
The ship’s crew were alerted and were ordered to make an immediate search of the area; so far the search has been un-successful.
A statement from P&O Cruises said: “We can confirm a missing female presumed overboard from Aurora sailing from Oporto to Barcelona. The ship turned round to search for her and all relevant authorities have been advised.
“Aurora is on a 14-night Western Mediterranean cruise which left Southampton on Wednesday September 26. Our care team is supporting the family and offering assistance.”
19:09PM Update – It has been confirmed in the last hour or so that the body of the missing passenger has been found by rescuers. Very sad indeed and my thoughts go out to her family.