The Communication Workers Union (CWU) said it was campaigning to save a “great British institution”.
Demonstrations were held at almost 50 locations, supported by Labour politicians and local campaigners.
The union is also gathering names for a petition it hopes will lead to the future of Post Offices being debated in Parliament.
The union says that when Crown offices - larger branches usually sited on high streets - close, many staff leave the service, and jobs advertised by firms such as WH Smith are paid lower than those at the Post Office.
CWU general secretary Dave Ward said: “The day of action is an ambitious one. We are holding dozens of events from Truro to Aberdeen, in every region of the United Kingdom, to engage with members of the public about this latest shameful round of planned closures.
“People are sick and tired of the broken privatisation agenda that is behind this latest move. We hope many will join our campaign to save our Post Offices.”
Deputy general secretary Terry Pullinger added that the Post Office should never have been separated from the privatised Royal Mail.
A WH Smith spokesman said: “We have successfully operated Post Offices in our stores since 2006 and are pleased to support a sustainable Post Office network.
“We work hard to ensure that customer service and accessibility is not just maintained, but improved.
“Post Offices are a vital hub providing essential services to the community and we take the social responsibilities associated with this very seriously.”
Roger Gale, the Post Office’s Network sales director, said: “The Post Office has over 11,500 branches across the UK. It will be business as usual in all our branches and we hope the CWU will ensure that there is no impact on customer service.
“The Post Office is committed to keeping its vital services on high streets and at the heart of communities across the UK. However, we are not immune to the challenges facing retailers in local high streets, and we must adapt to changing customer needs by making our services more accessible to customers, for instance through longer opening hours.
“That is why we are proposing to franchise a further 74 directly managed Branches to WH Smith.
“The plan enables us to maintain branches in town and city centres in a way that’s financially sustainable, not just for today’s customers but tomorrow’s too. 98% of the Post Office network is run in this way, on an agency or franchise basis. It’s a model that works through delivering the benefits of shared overheads and footfall.”