IANAL, but as far as I understand, details of all court records are considered as public records
Your question intrigued me – I did a bit of Googling, and found the National Archives website. I did an Advanced Search, using the date range 1977 – 1979, and the keywords “Leeds”, “Court” and “Manslaughter”, and came up with the following results:
http://discovery.nationalarchives.gov.uk/results/r?name=Search&_aq=leeds&_ep=&_or1=court&_or2=manslaughter&_or3=&_nq1=&_nq2=&_nq3=&_cr1=&_cr2=&_cr3=&_dss=range&_sd=1977&_ed=1979&_hb=&_ro=any&_rd=&_rsd=&_red=&_st=adv&_rv=
The National Archives is at Kew, and as well as being able to search online, you can go there in person. However, some records aren’t held at Kew
This is borne out by the specific entry for Leeds Magistrates Court records, which are physically held in Leeds (not surprisingly)
http://discovery.nationalarchives.gov.uk/details/a/A13531670
As far as I understand it, for a serious crime like manslaughter, the defendant would initially be charged in the magistrate’s court, but the trial would probably take place in the crown court, so you may need to search in both sets of records
Thinking laterally, it’s likely that such a case would have been covered extensively in the local press. I’m not local to Leeds, but there may be a local paper that keeps an archive. Leeds University may also keep an archive of local press cuttings (or the city library). Being physically in Leeds would definitely help your search!
By the way, shouldn’t this thread be in the Chat forum?
Does any of this help?