I just got an email that they are now taking bookings for March and April and that includes the Hidden Highlights tour, which I have read about. If you book this tour, you do not need to book a separate tour for the Queen’s Diamond Jubilee Galleries, as it is included in the HH tour.
From everything I have read, tickets for the HH tours go very quickly (not sure about March and April but I wouldn't chance it). They only have 2 tours a day. https://www.westminster-abbey.org/abbey-events/special-tours-and-events/2024/march/hidden-highlights-tour-march-2024#i23032
On this 75-minute tour you will visit areas of the Abbey not normally open to the public. You will see the lost medieval sacristy, recently revealed during one of our biggest ever archaeological projects, along with the following:
Florence Nightingale & Nurses' chapel, the chapel remembers those in nursing professions who died during the 1939-1945 war
Queen’s Diamond Jubilee Galleries, which displays many of the Abbey’s treasures
Jerusalem Chamber, the medieval room where Henry IV died and Henry V became king