The GRO Death Index has recently been updated to cover deaths from 1984 to 2019 although the index only gives year of birth and not full d.o.b.
It's free to search, although you need to register.
Still a gap between 1957 and 1984, but FreeBMD has that pretty much covered.
https://www.gro.gov.uk/gro/content/certificates/indexes_search.asp