Blood transfusion workers were set to strike from Wednesday to Friday of next week against the threatened closure of the Colindale centre, north London. They are members of the Unite union.
Workers at centres in Bristol and Manchester are also set to impose an overtime ban from Wednesday to Sunday.
The Filton centre, Bristol, is supposed to take on the workload arising from the closure. But it was forced to shut for all of last week due to heavy rain, which doubled the workload at Colindale and quadrupled it in Manchester.