National Probate Calendar has Thomas Edwin Cochrane of 14 Heathville Road, Gloucester retired shopkeeper who died 22 January 1901. Administration 19 April 1901 Gloucester to Charles Edward Cochrane Surgeon.
England & Wales Civil Registration Death Index, 1837-1915 has Thomas Edwin Cochrane, Birth abt 1834, Death 01/1901 Gloucester, Gloucestershire.
If the above is your Thomas Edwin Cochrane I don't think he would have been in the 1901 England Census which was taken on 31 March 1901.