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I travel with P&O on a regular basis and always have single occupancy of a twin cabin. Whilst I have an inside cabin, (to keep the costs down) I do know that P&O will accept bookings for Outside (even Balcony) cabins for single occupancy. However, you need to book very early (i.e as soon as the bookings are taken after the brochure launch), to get the best deals. This can mean booking anything up to 18 to 24 months in advance. After this the single occupancy supplement rises quite sharply.
I hope this helps.
Have just booked with P & O who charge 60% supplement for single occupancy. This is steep, but have standard double outside cabin, hopefully not in grotty part of ship. Single travellers get ripped off in the same way on land where hotels charge big supplements.
The best thing to do is pre book your cabin , agents have access to the dimensions of each cabin , this will help yo.