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Your first plan of action should be to explore Birmingham Mail archives I would say , I'm sure there must be an archive division . You might get somewhere by ringing the Mail up after all they are based at Fort Dunlop now they may give you some information . Can I just say while serving my apprenticeship in the 60's at the Post and Mail I had ocassion to look at some of the back issues of the Mail going back years and I mean years , there were great tomes of them . I could still be there today only I had to move on.
I searched on the words Kingshurst Meriden fire between 1 July 1968 and 30 June 1970 for newspapers published in Birmingham. Only the Birmingham Daily Post revealed any entries, but none involved a fire or a death. So it is possibly as you say in the Birmingham Mail, which is not online and if you go to Birmingham Archives, will not be indexed. That's an awful lot of issues to wade through day by day.
If you have a surname, I'm happy to do a further search.
I searched on Thomas Moore from 1st June 1969 to 31st December 1969, no location. Got plenty of Thomas Moores in Ireland, but the closest I got to Meriden was an incident about a dog in West Bromwich, when Sir Thomas Moore, President of the RSPCA was mentioned.
But you've got a death date, so a trawl through the Birmingham Mail in Birmingham Archives shouldn't be too extensive. Good luck.
I did check the Warwickshire deaths for 1969 and there is only one, with no other forenames, so it's likely reported in one of the local papers if only a Coroner' Report s. Hence, my wider search, but the Daily Post is the only one online after 1950. Most of the Thomas Moores were probably Catholics who came over in the 1800s I guess.