If you are allocated to the Britannia restaurant, it would not be possible for you to dine in the Princess Grill or Queens Grill as these restaurants are reserved for those guests travelling in Princess Grill or Queens Grill suites. It is also not possible for you to upgrade to dine in Princess Grill or Queens Grill restaurants, unless you upgrade your stateroom prior to sailing.
If you wish to dine with other guests who are booked into a different stateroom category you would all need to be booked into the same stateroom category.