Kelly's 1881 edition of the Directory of West Riding of Yorkshire explains:
The General Post Office, in Market street, is a handsome building of red brick, with stone dressings, opened August 1st, 1876.... and lists:
Post, Money Order & Telegraph Office, Savings Bank & Government Annuity & Insurance Office, Market street (next to the United Methodist Free Church).There were several architects in Wakefield in the 1870s, including William Crutchley (King street), Hammerton Lees (Lord Rodney yard, Westgate), Frederick Robinson (131 Northgate) and William Watson (Barstow square).
Postmaster - Richard Wilkinson Aspdin (Residence: York street, Northgate)
The photographer Warner Gothard advertised studio premises at "King Street & Wood St." Since the architect William Crutchley also had premises on King Street, it would be tempting to assume that he was the one to commission this cdv. However, Westgate, Northgate and Barstow square were all nearby, so it is more realistic to consider all four as potential architects of the Wakefield Post Office until further information is found.
Post Script - 31 August 2008
Nigel's photo (see comment)