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Cunard offer a 'White Star Luggage Service'. It is advertised as the perfect alternative to transporting your own luggage through airport and customs formalities. Shipment is provided by DHL Worldwide Express and is available exclusively for Cunard guests. Reservations must be secured at least 30 days prior to your sailing date. Domestic and international shipping is available. If you have already booked with Cunard you will find details of the luggage service included with the preliminary documents for your cruise. These are sent to you about eight weeks before your departure date. Alternatively, give Cunard a call.
There was a TV report on this last year, apparently they are a LOT more reliable than airlines etc and will collect and deliver almost anywhere. A search on courier +luggage +uk should do the trick.