Sadie Beal`s book on the Grimsby Workhouse says it officially opened in October 1894 and the Brighowgate Home in 1913, no month given.
She also states that children lived at Workhouse under the care of Nursery Nurses until the age of 3, but my relative remembered that he went to Brighowgate aged 5.
North East Lincs Archives will be able to give you more information, but a lot of the records are still under the 100 year closure.