This is most surprising and disconcerting. Usually, the guest relations people at Cunard are quite good and easy to speak with (although they doe not always agree to requests by passengers). Three thoughts come to mind.
First, if you booked this through a travel agent (and I hope you did), please have that travel agent work with Cunard. In a situation like this, a good TA can be worth his/her weight in gold.
Second, you should consider trying to get on a priority list for an "upgrade" to the proper size cabin. On the world cruise segments, there are quite often many unsold cabins and, thus, an upgrade is entirely possible.
Third, a very concise but persuasive letter addressed to the President of the compan (copy to your district sales manager) setting forth the problema and the requested resolution. Although this may be bucked down to the guest relations people, this kind of thing is always better in writing.
Whatever you do, please do it quickly as the World Cruise starts very soon.
And, however this works out, have a wonderful trip.