sorry to resurrect a zombie thread, but I have the answer - worked for me!
seeking out the naturalisation records for my late grandfather which were closed until 2032. Sent an FOI request, citing the need to know of his children (my father and aunts) all in their 80s. Waited for the approved time, the records were then opened. Got a quote, paid and a fascinating envelope arrived. You pay per page, I think it was well under £20.
as always, more questions than answers but we found out a lot.
I have a similar issue relating to a criminal case but no one is in touch with the family member who would be 97 now which is possible, but her parents and all her siblings died before 70. The issue for me is that I believe there was a marriage but have no idea to who and this cannot prove that she is dead. The records I need are closed until 2037 because it is 100 years from the incident.