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Mohammed Saddiq Khan, a 30-year-old man, is thought to be have been responsible for the Edgware Road attack.
Khan lived in a council house in Lees Holm, Dewsbury, with his wife Hasina and baby girl who was born late last year. Local people said that the couple had moved there this year from nearby Leeds, where Khan owned a book shop.
His wife is believed to have reported Khan missing last week. It is thought that Hasina was a neighbourhood enrichment officer working with children in schools before having her baby.
Neighbours said the couple were not well known in the community.
Farida Patel, Khan’s mother-in-law, who lives with her 28-year-old son Arshad in Dewsbury, is well known for her work in the local community.
Yunus Patel, 32, a neighbour, said: “His mother-in-law was a very strong woman. She was well known in the community and had been to Buckingham Palace.”