I've now scoured the local 'papers, Beckenham & penge Advertiser and Beckenham Journal, immediately after those dates, without finding anything.
He was at Anerley House in the first post-WW2 electoral roll, qualifying date 30-Jun-1945, so probably one of its first residents when it opened at the end of the war as a retirement home in the former North Surrey District School building. Initially it was for men only, so if he'd acquired another wife since he left your grandmother, she was longer with him.
I've looked without success in all the directories covering Beckenham & Penge from 1922-39 and also the 1939 electoral roll, though as the roll isn't indexed by name I might have missed him. With nearly 250 residents and near the meeting-point of 5 local authorities, it's likely the home had a wide catchment area.
I think the best bet is to wait for the National Registration data to go online, which will narrow down the search a bit.