The unions has accused ministers of refusing to negotiate over its economic and social policies.
Unite General secretary Len McCluskey said:
Our members at HCA are showing solidarity with their HCA colleagues in PCS against the savage attack by the coalition on public services and those dedicated staff that deliver them.
The anger is growing at the negative dead end economic and social policies of this right-wing government - from the easy ride that the City elite receives from George Osborne to the gross unfairness of the hated bedroom tax which will hit 650,000 people.
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The operation to recover the unexploded bomb near the Houses of Parliament let to disruption in central London overnight.
Southern parts of England and Wales will see sunny skies after a frosty start.
A police spokesman said the incident in the Bourke Street Mall on Friday was not related to terrorism.