The old newspapers are stored at Carlisle library on microfiche. The library is undergoing a refurbishment and is operating at a reduced level, so currently the newspapers aren't available and the Carlisle Archives only hold a limited amount of old newspapers on microfiche, unfortunately not from this time period.
If he was buried in Carlisle, it would be in one of three municipal cemeteries and as he lived in Highwood Crescent, Harraby would, I think be either Upperby (closest) or the largest cemetery on Dalston Road. You could contact
Cemetery & Crematorium Office
Carlisle Crematorium
Dalston Road,
Carlisle,
CA2 6AT
Tel: 01228 817390
for information about his possible burial or cremation.
Carlisle Archives do have records for the municipal cemeteries but I think they only go up to the very early 60's, so if his wife died in 1959, they may hold the record for that and her place of burial might give you a clue to where he was buried. I can check this for you on my next visit, (probably in the next few weeks)
I can also check the newspaper for both death and sympathy announcements when the library reopens fully and the records are available again.