There are no single cabins on RCI, so you would have a double cabin for sole occupancy. You will pay a premium of around 150%.
Afraid so can vary between 20 and 75% and Royal Caribbean on one site were quoted at 200% but with certain of their ships on certain cruises a lot lower so you need to contact a specialist cruise advisor try the number above 0800 091 1629. I use them and they are very good.
Royal Caribbean - Independence of the Seas - 14 Oct 17 - 7nts
Southampton : Gijon : Bilbao : Cherbourg : Paris (Le Havre) : Southampton
Now from £579pp
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P&O Cruises - Ventura - 13 Nov 17 - 11nts
Southampton : Lisbon : Valencia : Cartagena : Gibraltar : Seville (Cadiz) : Southampton
Now from £599pp Was £639pp
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Princess Cruises - Caribbean Princess - 20 Apr 17 - 11nts
Southampton : Guernsey : Cork : Dublin : Hamburg : Rotterdam : Brussels : Paris : Southampton
Now from £999pp Was £1329pp
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