Under the plans Crown Post Office branches, including in Beverley, Harrogate, Northallerton, Scarborough, Selby and York, will move into the High Street retailer.
Across the country around 700 Post Office jobs face an uncertain future, as a result of the proposals to franchise more than 70 branches.
York MP Rachael Maskell said the proposal to move the Post Office at 22 Lendal, one of the last surviving late-Victorian purpose-built post offices still in use today, was driven by "ideology not common sense" and there should have been consultation first.
She said staff would be uncertain about their futures, while residents and businesses would be infuriated.
She said: "Every city centre should have a Crown Post Office, but to lose this vital service in a city such as York is a travesty.
"It downgrades the importance of York, and it demonstrates contempt for residents.
"Local residents as well as tourists use Lendal Post Office, which provides a range of services from the highly professional staff who work there."
Beverley and Holderness MP Graham Stuart said he would "take a lot of convincing" given the queues already in the WH Smith's on Toll Gavel in the town.
Ward councillor Elaine Aird said the plans were "ludicrous." She said it was busy with residents and also businesses, adding: "I fail to see how this large volume of work can be carried out in W H Smith which is, after all, a rather small shop.”
As well as the plans to relocate 40 Post Offices into WHSmith, 33 more branches, which are already in the stores, but still operated by the Post Office, will also be franchised.
The CWU union's national officer Andy Furey said the move equated to almost one-third of the network.
He said franchising was “privatisation by the back door" and there had been no engagement with the union which was preparing to mount a vigorous campaign against this "catastrophic action.”
He said: “This is a massive slap in the face for our members who will be devastated especially as they have worked so hard and sacrificed so much to return the Crown Network to profitability.”
Post Office Network and Sales Director Roger Gale said: “WHSmith and Post Office have worked together successfully for more than a decade and our collaboration helps to secure our services on high streets for years to come.
“We’re continuing to respond to unprecedented change on high streets and in consumer trends. By adapting to the needs of customers we’re making sure Post Offices will matter as much tomorrow as they do today, with services available when and where people want them, in convenient locations and open for longer hours, including Sundays."